Back and Forth Motion in Kinematics Graphs

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太极拳英文基本术语

太极拳英文基本术语掤、捋、挤、按、採、挒、肘、靠、进、退、顾、盼、定 Peng (warding off), Lv (rolling back), Ji (pressing), An (pushing), Cai (pulling down), Lie (splitting), Zhou (elbowing), Kao (body stroke), Jin (advancing), Tui (retreating), Gu (shifting left), Pan (shifting right) and Ding (central equilibrium)不丢不顶 no releasing and resisting directly不解之谜 mystery不偏不倚 impartiality缠丝 twining沉肩坠肘 lowering the shoulders and elbows沉着 heavy and steady撑掌 unfolding palm成语之都 Hometown of Chinese Idioms抽丝 taking out the thread丹田 Dantian (pubic region)弹簧力 springy force导引术 guidance道 Tao;Dao道法自然 Taoism following the nature敌进我退，敌驻我扰，敌疲我打，敌退我追 retreating as the enemyadvances, disturbing as the enemy camps, attacking as the enemy fatigues, advancing as the enemy retreats第五代传人 fifth-generation successor顶头悬 suspending the head and relaxing the neck懂劲 comprehending force动与静 motion and stillness动中寓静 stillness with motion动作 action动作／招式／招术 movement/action对立统一 the unity of opposites对立与统一 contradition and unfication;unity of the opposites 耳提面命 whispering into disciples’ ears and talking face to face发劲 discharging force法道修身 self-cultivation with Tao法道治国 state-governing by Tao反者道之动，弱者道之用 The application of Dao is using mildness rather than violence, softness rather than hardness非圆即弧 either circle or arc刚柔相济 combining hardness with softness根于脚，主宰于腰，行于手指 rooting with feet, leading with waist, and moving with fingers弓步 n.bow stance; v.lunge forward功夫 Gongfu; Kungfu;fighting art;fighting skills攻防 attack and defense; offense and defense攻防搏击 offensive and defensive fighting贯串之意 Yi of permeating国术馆 National Martial Arts Gyms含胸拔背 contracting the chest and lengthening the back合中有开 closing with opening后发制人 striking only after being struck呼、发、伸、进、起、仰、往、出、放、打、击、刚、动、实、开、升、上、左 breathing out, attacking, extending, advancing, raising, facing upward, going, sending, releasing, hitting,striking, hardness, moving, solidness, opening, lifting, ascending,turning left呼与吸 breathing out and breathing in化劲 dispersing force技击术 art of attack and defense节节贯串 joints’ coordinating借力打力 transforming the coming force to attack the opponent 劲整 integrating force经络 Jingluo (main and collateral channels)经络中通行的气 Qi (air) in Jingluo精神 mind静中寓动 motion with /in stillness卷（蓄）与放 storing and discharging开胯屈膝 separating the thighs and bending the knees开与合 opening and closing开中有合 opening with closing快与慢 rapidness and slowness老子学说 Laozi’s Doctrines砺练品格 morality training练劲 building up power练巧 mastering techniques练顺 smoothing out the frame螺旋 volution螺旋缠绕 spiral enwinding落点（劲点） attacking points （positions）门规戒条 doctrines, regulations and restrictions内不动，外不发 no internal Yi (mind), no external movements 内劲 Neijin (inner power)内劲潜换 inner power exchanging内气 Neiqi (inner air)内外皆修 internal and external cultivation内外统一 uniting mind with body偏心距 eccentric distance平和安静，谦和大度，博爱真诚，感恩包容 gentleness and peace, modesty and generosity, love and sincerity, gratitude and tolerance平心静气 calming mind气沉丹田 Qi Chen Dantian (storing qi in the pubic region）气敛 Storing Qi (spirit;air)牵一发而动全身 a slight move in one part may affect the whole situation乾坤 Qiankun (heaven and earth, the universe)强身健体 body building and physical fitness窍 aperture轻灵 agile轻与沉 lightness and heaviness全国武术锦标赛 Championship of National Martial Arts拳法 boxing method拳理 boxing theory拳式 movement拳姿 boxing posture人不犯我、我不犯人、人若犯我、我必犯人 We will not attack unless we are attacked; if we are attacked, we will certainly counterattack.柔与刚 softness and hardness儒雅端庄 refined and dignified散手 San Shou (free sparring)上下相随 the harmony between the upper and lower body舍己从人 giving up one’s own to accept the widely-accepted one 身心双修 physical and spiritual cultivation神 Shen (concentration of the mind)神聚 concentrating the attention神明 sprirtual illumination十大文化脉系 ten major regional cultures十三势 Thirteen (13) Postures收敛入骨 storing in the body疏通经络 activating channels四两拨千斤 defeating the strong with little effort松静自然 being natural, relaxed and quiet松柔缓慢 soft and slow松腰圆裆 relaxing the waist and separating the thighs宋明理学 Neo-Confucianism太极拳 Taijiquan;Tai Ji Quan;Tai Chi;Taiji boxing;Shadow boxing 太极拳圣地 Hometown of Taijiquan太极拳小架子 the small frame of Taijiquan太极图 Taiji Diagram陶冶情操 molding character套路 routine体育运动学 sports and kinematics天地与我并生，万物与我为一。

太极拳英文基本术语

太极拳英文基本术语；掤、捋、挤、按、採、挒、肘、靠、进、退、顾、盼、；不丢不顶noreleasingandresist；不解之谜mystery；不偏不倚imp art iality；缠丝twi ning；沉肩坠肘loweringtheshoulders；沉着heavyandsteady；撑掌unfoldingpalm；成语之都HometownofChineseId太极拳英文基本术语掤、捋、挤、按、採、挒、肘、靠、进、退、顾、盼、定 Peng (warding off), Lv (rolling back), Ji (pressing), An (pushing), Cai (pulling down), Lie (sp litting), Zhou (elbowing), Kao (body stroke), Jin (advancing), Tui (retreat ing), Gu (shifting left), Pan (shifting right) and Ding (central equilibriu m)不丢不顶 no releasing and resisting directly不解之谜 mystery不偏不倚 imp art iality缠丝 twining沉肩坠肘 lowering the shoulders and elbows沉着 heavy and steady撑掌 unfolding palm成语之都 Hometown of Chinese Idioms抽丝 taking out the thread丹田 Dantian (pubic region)弹簧力 springy force导引术 guidance道 Tao;Dao道法自然 Taoism following the nature敌进我退，敌驻我扰，敌疲我打，敌退我追 retreating as the enemyadvances, disturbing as the enemy camps, attacking as the enemy fatigue s, advancing as the enemy retreats第五代传人 fifth-generation successor顶头悬 suspending the head and relaxing the neck懂劲 comprehending force动与静 motion and stillness动中寓静 stillness with motion动作 action动作／招式／招术 movement/action对立统一 the unity of opposites对立与统一 contradition and unfication;unity of the opposites 耳提面命whispering into disciples’ ears and talking face to face发劲 discharging force法道修身 self-cultivation with Tao法道治国 state-governing by Tao反者道之动，弱者道之用 The application of Dao is using mildness rather than violence, softness rather than hardness非圆即弧 either circle or arc刚柔相济 combining hardness with softness根于脚，主宰于腰，行于手指 rooting with feet, leading with waist, and m oving with fingers功夫 Gongfu; Kungfu;fighting art;fighting skills攻防 attack and defense; offense and defense攻防搏击 offensive and defensive fighting贯串之意 Yi of permeating国术馆 National Martial Arts Gyms含胸拔背 contracting the chest and lengthening the back 合中有开 closin g with opening后发制人 striking only after being struck 呼、发、伸、进、起、仰、往、出、放、打、击、刚、动、实、开、升、上、左 breathing out, attacking, extending, advancing, raising, facing upward, going, sending, releasing, hitting,strik ing, hardness, moving, solidness, opening, lifting, ascending,turning left 呼与吸 breathing out and breathing in化劲 dispersing force技击术art of attack and defense节节贯串joints’ coordinating借力打力 transforming the coming force to attack the opponent 劲整 inte grating force经络 Jingluo (main and collateral channels)经络中通行的气 Qi (air) in Jingluo静中寓动 motion with /in stillness卷（蓄）与放 storing and discharging开胯屈膝 separating the thighs and bending the knees 开与合 opening and closing开中有合 opening with closing快与慢 rapidness and slowness老子学说Laozi’s Doctrines砺练品格 morality training练劲 building up power练巧 mastering techniques练顺 smoothing out the frame螺旋 volution螺旋缠绕 spiral enwinding落点（劲点） attacking points （positions）门规戒条 doctrines, regulations and restrictions内不动，外不发 no internal Yi (mind), no external movements 内劲 Neijin (inner power)内劲潜换 inner power exchanging内气 Neiqi (inner air)内外皆修 internal and external cultivation内外统一 uniting mind with body平和安静，谦和大度，博爱真诚，感恩包容 gentleness and peace, modesty an d generosity, love and sincerity, gratitude and tolerance平心静气 calming mind气沉丹田 Qi Chen Dantian (storing qi in the pubic region）气敛 Storing Qi (spirit;air)牵一发而动全身 a slight move in one part may affect the whole situation 乾坤 Qiankun (heaven and e art h, the universe)强身健体 body building and physical fitness窍 aperture轻灵 agile轻与沉 lightness and heaviness全国武术锦标赛 Championship of National Martial Arts 拳法 boxing method 拳理 boxing theory拳式 movement拳姿 boxing posture人不犯我、我不犯人、人若犯我、我必犯人 We will not attack unless we are attacked; if we are attacked, we will certainly counterattack.儒雅端庄refinedanddignified；散手SanShou(freesparring)；上下相随thehar monybetweenthe；舍己从人givingupone’sowntoac；神Shen(concentrationofthe；神聚concentratingtheattent；神明sprirtualillumination；十大文化脉系te儒雅端庄 refined and dignified散手 San Shou (free sparring)上下相随 the harmony between the upper and lower body舍己从人giving up one’s own to accept the widely-accepted one 身心双修 physical and spiritual cultivation神 Shen (concentration of the mind)神聚 concentrating the attention神明 sprirtual illumination十大文化脉系 ten major regional cultures十三势 Thirteen (13) Postures收敛入骨 storing in the body疏通经络 activating channels四两拨千斤 defeating the strong with little effort松静自然 being natural, relaxed and quiet松柔缓慢 soft and slow松腰圆裆 relaxing the waist and separating the thighs 宋明理学 Neo-Conf ucianism太极拳 Taijiquan;Tai Ji Quan;Tai Chi;Taiji boxing;Shadow boxing 太极拳圣地 Hometown of Taijiquan太极拳小架子 the small frame of Taijiquan太极图 Taiji Diagram套路 routine体育运动学 sports and kinematics天地与我并生，万物与我为一。

故宫可以怎么写作文英语

The Forbidden City, a masterpiece of Chinese architecture and a symbol of imperial power, has always been a source of fascination for me. As a high school student with a keen interest in history and culture, I have always been eager to explore the stories and secrets hidden within its ancient walls. In this essay, I will share my experience of visiting the Forbidden City and reflect on its significance in Chinese history and culture.My journey to the Forbidden City began on a crisp autumn day. As I stepped through the grand entrance, the Meridian Gate, I was immediately struck by the sheer scale and grandeur of the complex. The vast expanse of red walls and yellowtiled roofs stretched out before me, a testament to the architectural prowess of the Ming and Qing dynasties. The air was filled with a sense of awe and reverence, as if the very stones and bricks whispered tales of the past.As I wandered through the palace grounds, I was captivated by the intricate details and designs that adorned the buildings. The dragon motifs, a symbol of imperial authority, were carved into the eaves and pillars, their scales shimmering in the sunlight. The vibrant colors of the murals and paintings depicted scenes from Chinese mythology and history, bringing the stories to life. Each corner and corridor seemed to hold a new discovery, a glimpse into the lives of the emperors and their court.One of the highlights of my visit was the Hall of Supreme Harmony, the largest and most important hall in the Forbidden City. It was here that the emperors held grand ceremonies and audiences, asserting their divine right to rule. The halls majestic throne, adorned with a dragon canopy,exuded an air of power and majesty. I could almost imagine the emperor seated there, receiving tributes from his subjects and foreign envoys.Another fascinating aspect of the Forbidden City is its layout and design. The complex is meticulously planned, with the central axis running from north to south, symbolizing the emperors connection to the heavens. The buildings are arranged in a series of courtyards and gates, each with its own purpose and significance. This architectural harmony reflects the Confucian ideals of order and hierarchy that were deeply ingrained in Chinese society.However, the Forbidden City is not just a symbol of imperial power it is also a treasure trove of Chinese art and culture. The palaces house a vast collection of artifacts, including porcelain, jade, calligraphy, and paintings, showcasing the artistic achievements of the dynasties. As I marveled at the delicate craftsmanship and intricate designs, I gained a deeper appreciation for the rich cultural heritage of China.Despite its grandeur, the Forbidden City also serves as a reminder of the harsh realities of imperial life. The concubines and eunuchs who lived within these walls faced a life of intrigue and power struggles. The strict social hierarchy and rigid court rituals must have been suffocating for those who were not part of the ruling class. In this sense, the Forbidden City is a microcosm of the broader social structure of ancient China.In conclusion, my visit to the Forbidden City was an unforgettable experience that deepened my understanding of Chinese history andculture. The architectural splendor, artistic treasures, and historical significance of the complex left a lasting impression on me. As I walked through the gates and back into the bustling streets of Beijing, I felt a sense of gratitude for the opportunity to explore this unique window into the past. The Forbidden City is not just a monument to the past it is a living testament to the enduring legacy of Chinese civilization.。

机械专业英语备考句、段翻译【池院2014版】

第一课：Basic Concepts in Mechanics力学基本概念①The branch of scientific analysis which deals with motions, time, and force is called mechanics and is made up of two parts, statics and dynamics.【对运动、时间和作用力进行科学分析的分支称为力学，它由静力学和动力学两部分组成。

】②For example, if the force operating on a journal bearing becomes too high, it will squeeze out the oil film and cause metal-to-metal contact, overheating, and rapid failure of the bearing.【例如，如果作用在一个滑动轴承上的力太大，它就会将油膜挤出，造成金属与金属的直接接触，产生过热并使轴承快速失效。

】（（要求看一下的：（牛顿三定律）③Law 1If all the force acting on a particle are balanced, the particle will either remain at rest or will continue to move in a straight line at a uniform velocity. [如果作用在一个物体上的所有的力平衡，那么，这个物体将保持原来的静止或匀速直线运动状态不变。

]Law 2If the forces acting in a particle are not balanced, the particle will experience an acceleration proportional to the resultant force and in the direction of the resultant force.[如果作用在一个物体上的那些力不平衡，那么，这个物体将产生加速度。

论弗罗斯特《摘苹果之后》中的死亡隐喻

论弗罗斯特《摘苹果之后》中的死亡隐喻发布时间：2022-07-21T08:53:03.876Z 来源：《时代教育》2022年5期作者：刘沛婷[导读] 乔治·莱考夫和马克?约翰逊于《我们赖以生存的隐喻》一书中指出隐喻不仅仅是一种修辞手法，更是一种思维方式刘沛婷湖南师范大学，湖南长沙 410006摘要：乔治·莱考夫和马克?约翰逊于《我们赖以生存的隐喻》一书中指出隐喻不仅仅是一种修辞手法，更是一种思维方式，在人们的日常语言和活动中无所不在。

诗歌是高度隐喻化的体裁，本文就将以弗罗斯特的短诗——《摘苹果之后》为例，通过挖掘诗歌中的结构隐喻、方位隐喻和本体隐喻，深刻剖析弗罗斯特的死亡观建构，为该诗的解读提供新的维度，也有助于丰富该理论的应用范畴。

关键词:《摘苹果之后》；结构隐喻；方位隐喻；本体隐喻；死亡On death metaphors in Frost’s “After Apple-Picking”Peiting LiuHunan Normal University, Hunan Changsha 410006Abstract: George Lakoff and Mark Johnson put forward in their book Metaphors We Live By that metaphor is not only a figure of speech but a way of thinking, pervasive in everyday language and action. Since poetry is highly metaphorical, this thesis is to explore how Robert Lee Frost construct his insight of death through structural metaphors, orientational metaphors as well as ontological metaphors in his short poem “After Apple-Picking”, with the hope to provide a new dimension for the interpretation of the poem and to expand the application scope of the theory. Key words: “After Apple-Picking”; structural metaphors; orientational metaphors; ontological metaphors; death 1.IntroductionLakoff and Johnson in their monograph Metaphors We Live Вy, point out that metaphor not only can be understood from the figurative perspective, but is the thinking way.[1] Ungerer and Schmid hold that conceptual metaphor, as a cognitive instrument, is not just a stylistically dramatic way of expressing thoughts by means of literary language, but a way of thinking.[2] K?vecses has put that conceptual metaphor is defined as understanding one conceptual domain in terms of another conceptual domain.[3] On the basis of the cognitive approach to the understanding of conceptual metaphor, it can be divided into structural metaphor, orientational metaphor and ontological metaphor. The development of conceptual metaphor theory has brought advance to Linguistics, Anthology, Literature and so on.Robert Lee Frost commands an important place in any list of outstanding poets in the twentieth century. His poem “After Apple-picking” is written in the first person. The speaker is an orchard worker who has picked apples long and hard but is now on the verge of being overwhelmed by fatigue and the depth of the experience. On the edge of falling sleep, he remembers not only the ripe apples successfully picked but also those that fell and were considered damaged and had to be sent to the cider mill. He knows that his sleep will be troubled by the failures more than by the successes. He is not sure about the nature of the sleep he is about to drop into—whether it will be ordinary sleep, more like a hibernation, or more like death.The entire poem is a kind of extended metaphor, in which the activity of harvesting apples represents people’ life and the speaker’s falling asleep suggests human death.As a classical literary work, the study of this poem mostly focuses on its rhythm and writing devices. The analysis of multiple themes and symbols has always been the research hotspot of literature works. Li Yingxue discussed the fuzziness of the meaning of poetry from the perspective of deconstruction, and there are many scholars who explore metaphors in Frost’s other poems.[4] Few people applied it to analyze “After Apple-Picking”. Therefore, this paper is to discuss how Frost structures his thoughts on death metaphorically by describing a laborer’s picking apples. The first three chapters of this thesis illustrate Frost’s views of death through the construction of structural metaphors, orientational metaphors and ontological metaphors in “After Apple-Picking” respectively. At last it is followed by a logical conclusion of this thesis.2.Structural MetaphorsIn structural metaphor, one greatly structured and explicitly delineated concept is applied to structure another. As Lakoff and Johnson point out that one domain of conceptual metaphor is metaphorically structured in light of another. Structural metaphor allows its source domain to offer a comparatively rich knowledge structure for the target domain, that is to say, the cognitive function of structural metaphor is to enable audiences to understand the target domain by the structure of the source domain. The poem “After Apple-Picking” include two key conceptual metaphors: DEATH IS SLEEP and PEOPLE ARE PLANTS.2.1 DEATH IS SLEEPFrost chooses a laborer who is overtired with apple-picking and falls asleep to reflect his insight of death. Hence the poem can be understood as a mapping from a source domain (sleep) to a target domain (death). The mapping is tightly structured. There are ontological correspondences. The dead correspond to those who have a sound sleep. The retrospection before death corresponds to the unconscious state near sleep. The darkness corresponds to the night. The cease of life corresponds to the stillness and motionlessness of sleep. As Lakoff puts it, “people use a concrete source domain to describe an abstract target domain.”[5] Death is an abstract concept, which can be understood vividly through the concept of sleep. The word “sleep”has been repeated five times. “Winter sleep” suggests the emotion of being decayed, forlorn and silent triggered by death because winter, in the metaphoric meanings, has strong associations with death.[6] Another euphemistic expression of death is “long sleep”, which is indicative of its permanence. “Human sleep” is the most evident reflection of conceptualization of death as sleep, showing that human death is what Frost has discussed. In the light of sleep, Frost’s “After Apple-Picking” is no longer a lyrical poem of a worker’s experience on the orchard farm and fatigue aftera day’s labor, but a profound thought on life and death through an extended conceptual metaphor of death as sleep.2.2 PEOPLE ARE PLANTSBoth man and tree are living beings that go through birth and wither, and the achievements of man are kin to the fruits of plants. “Apples I didn’t pick upon some bough” correspond to those unfilled dreams while apples that “struck the earth/ No matter if not bruised or spilled with stubble”correspond to people’s failed pursuits. The scent of apples refers to delight and satisfaction brought by success. In Frost’s poem, the act of apple-picking is a metaphor for the fruits the speaker has achieved in life.[7] It is universally acknowledged that success is what people desire and is something enjoyable. However, the speaker is overtired of the great harvest and wished to rest, which illustrates that the speaker has been bored with worldly sense of accomplishment and hopes to simple have a dream and a “long sleep”. Due to the sweet smell of the apple, the narrator actually falls asleep after fatigue and he enters into “long sleep”(death) with a sense of emptiness resulted from the excessive fruits he has gathered. The speaker’s experience reveals the poet’s meditation on life that it is futile people achieve a great deal of success but eventually own nothing after death. Therefore, the poet don’t ponder on human sleep for no reason but he penetrates the meaninglessness of long tough life struggles.The two root metaphors are carefully chosen to reflect Frost’s philosophy on death. This also confirms the cognitive value of metaphor, that is, vehicles(such as sleep) are usually well known to readers, and their features and structures will be mapped to relatively unfamiliar things when they interact with tenor (such as death) to help readers understand the characteristics and structures of ontology. The characteristics of sleep are mapped to the characteristics of death. Frost’ poem “After Apple-Picking” is not only a pastoral work of rural world in orchard farm but also a thought-provoking poem on death. The end of labor leaves the speaker with a sense of completion and fulfillment yet finds him blocked from success by winter’s approach and physical weariness. The futility that what people achieved as a result resembles fallen apples of no worth leads to fatigue and wish to seek relief in sleep, that is death. Therefore, this seemingly idyllic poem is in fact the ultimate exploration of human destiny through the metaphors of death as sleep and people as plants.3.Orientational MetaphorsOrientational metaphors do not structure one concept in terms of another but instead organize a whole system of concepts with respect to one another.[1] Most of them have to do with spatial orientation: up-down, in-out, front-back, on-off, deep-shallow, central-peripheral. These spatial orientations arise from the fact that we have bodies of the sort we have and that they function as they do in our physical environment. As Lakoff points out that CONSCIOUS IS UP; UNCONSCIOUS IS DOWN. HEALTH SND LIFE ARE UP; SICKNESS AND DEATH ARE DOWN. This poem employs spatial antagonism to construct death metaphor. “The Apple-Picking” involves a development from consciousness to unconsciousness. At the very beginning, the farmer is sober enough on the long two-pointed ladder sticking toward heaven. The spacial position is rather high. After the speaker has been done with apple-picking, rest is badly needed after the arduous labour. He is drowsed off and no longer in his conscious state. Frost adopts simple past tense from line8 to line17, serving as a beginning of the speaker’s dream. In the half unconsciousness of the farmer, the autumn evening bursting with the aroma of the apples has for a moment changed into a winter morning with hoary glass. In farmer’s dream, things “melted”, “fall and break”, which suggests a downward trend. Finally both woodchuck and the farmer fall asleep on the ground. The perspective of the whole poem shifts from heaven to earth, that is from top to bottom, revealing the opposition of space. A pane of glass divides the world into two parts: reality and dream. The transition from reality to dream is the manifestation of change of the speaker’s consciousness. The higher position represents reality and consciousness while the lower dream and unconsciousnessWhat’s more, the positional contrast reveals the opposition of life and death. In the first line of “After Apple-Picking”, the ladder occupies a central position in the whole picture of the poem, acting as a bridge between heaven and earth, life and death. The imagery of heaven and apples evokes the garden of Eden. The act of ascending the ladder symbolized a re-approach to heaven and eternal life while the movement down the ladder symbolizes the descent from heaven to earth, also from life to death[4]. According to Bible, picking apples is considered as corruption and degradation. As baskets of apples fall down and are spiked, they become worthless. This is true of human beings. After the farmer has finished apple-picking, fatigue and emptiness has wrapped him. His vigorous life reaches a pause, which actually means the farmer’s death. Most of fundamental concepts are organized in terms of one or more spatialization metaphors. In Frost’s “After Apple-Picking”, the poet shows the transition from consciousness to unconsciousness as well as from life to death in virtue of the binary opposition of space. The physical basis of such division is that humans sleep and die lying down and stand up when they are awaken. Therefore, the antagonism of life and death is constructed through the opposition of up and down positions, which contributes to the further construction of the root metaphors.4.Ontological MetaphorsOntological metaphor helps us understand those abstract entities through conceptualizing them as these entities and substances which are related to human’s experience. As Lakoff and Johnson point out: “our experience of physical objects and substances provides a further basis for understanding.” Ontological metaphor could be classified into three types, which are entity and substance metaphor, container metaphor and personification.Firstly, an invisible abstract concept, in entity and substance metaphor, is considered as a visible concrete object. Human being expresses abstract concepts as these entities and substances which are related to human’s experience. Death is an abstract concept, which can be understood thanks to another common concept—sleep. The dark and bleak state of death is implied by night in winter. The poet also tries to clarify the hibernation of hamsters and the long sleep of human beings: one is short seasonal rest and the other is an eternal stop of motion. In this way, the characteristics of death are no longer vague. The first root metaphor of death as sleep receives deeper and more detailed illustrations. Similarly, human achievements becomes a measurable entity like apples in “ After Apple-Picking”. Through these well-known common things, the original abstract concept can be elucidated. The essence of metaphor lies in the comparison between two entities.Secondly, container metaphor is a kind of ontological metaphor in which an invisible abstract concept is regarded as a container which has a surface owning scope and range with an in-out orientation. In Frost’s poem, the farmer’s dream and sleep is a container, where he can see “magnified apples”, feel “the pressure of ladder-round”. The farmer’s falling into dreams shows the motion from one space to another space. The state of farmer can be classified into “in sleep” and “out of sleep”, which symbolize death and life respectively.Lastly, personification specifies the physical object as being a man, which can make people to comprehend these different physical objects in light of human characteristics, motivations and activities. In Frost’s poem, apple “struck the earth” and long sleep can “come on” are all personification. They are extensions of ontological metaphors and that they allow us to make sense of phenomena in the world on the basis of our own goals. It is carefully chosen to endow this poem a dynamic effect so that the theme of this poem can be effectively conveyed. All in all, the understanding of a poetic metaphor is a cognitive process.[8] Ontological metaphor makes us understand abstract concepts by use of concrete concepts. The poet uses sleep to explain death, making the abstract concept simplified and concrete. In the poem, the dream not only reflects the structural metaphor, but also reflects the container metaphor. It forms a contrast between “in dream” and “out of dream” so as to further strengthen the difference between life and death. Apple has bruises, and Death actively does come in. These anthropomorphic expressions embody the metaphorical nature of language and the symbolic nature of death. As a result, metaphor of death in this poem has been justified.5.ConclusionThe exploration of the relationship between Frost’s view of death and Lakoff’s cognitive metaphors will undoubtedly help readers to guard against deceptive surface meanings when interpreting and appreciating Frost’s poems, and to explore the profound life philosophy reflected in his poems through metaphorical thinking and active participation.Through dividing metaphors in Frost’s “After Apple-Picking” according to Lakoff’s classification, the way of constructing poem’s theme is evidently revealed. At the first glance, it seems to be a lyrical poem, but it actually a poem of death after further analysis. Frost implicitly depicts life actions as apple picking activities, apples are symbols of human achievements, and death is similar to long sleep, which are structural metaphors, through which the characteristics of abstract concept death can be easily understood. Moreover, the orientational metaphors constitute to the body of this poem. The up-down spatial position divides the farmer’s state into consciousness and unconsciousness, also a reflection of human’s state of life and death. The contrast between in-out categories reflects the whole poem’s structure: it shifts from reality to dream. Since the farmer’s dream is explained as a container, the state of dreaming metaphorically stands for death. Therefore the whole poem is based on structural metaphors of death is sleep and people are plants, which are illustrated with orientational metaphors and ontological metaphors.However, the thesis still has some limitations due to the author’s slim analysis. It can be better with more logical illustrations and evidences. But it is no doubt that the thesis provides a new perspective of discussing Frost’s poem. It expands the application scope of Lakoff’s conceptual metaphor and enriches its practice, and produces referential meaning to literature appreciation. References[1]Lakoff, G & M. Johnson. Metaphors We Live By[M]. Chicago: The University of Chicago Press.1980.[2]Ungerer, F & H. J. Schmid. An Introduction to Cognitive Linguistics.[M]. Beijing: Foreign Language Teaching and Research Press. 2008.[3]K?vecses, Z. Metaphor: A practical introduction[M]. New York: Oxford University Press.2002.[4]李应雪. 一个解构批评的范本——析罗伯特·弗洛斯特诗歌《摘苹果之后》意义的模糊性[J]. 宁夏大学学报(人文社会科学版), 2007(04): 78-81.[5]Lakoff, G. The Invariance Hypothesis: is abstract reason based on image-schemas?[J]. Cognitive Linguistics, 1990(01): 39-47.[6]Huo, Lirong. Comments on “After Apple-Picking”[J]. Overseas English, 2012(01): 196-197.[7]赵志宇. 罗伯特·弗洛斯特的《摘罢苹果》[J]. 文学语言学研究, 2007(02):70-71.[8]胡壮麟. 诗性隐喻[J]. 山东外语教学, 2001(03): 3-8.。

Inverse kinematics positioning using nonlinear programming for highly articulated figures

Inverse Kinematics Positioning Using Nonlinear Programmingfor Highly Articulated FiguresJianmin Zhao and Norman I.BadlerDepartment of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphia,PA19104-6389AbstractAn articulatedﬁgure is often modeled as a set of rigid segments connected with joints.Its conﬁguration can be altered by varying the joint angles.Although it is straightforward to computeﬁgure conﬁgurations given joint angles(forward kinematics),it is not so toﬁnd the joint angles for a desired conﬁguration (inverse kinematics).Since the inverse kinematics problem is of special importance to an animator wishing to set aﬁgure to a posture satisfying a set of positioning constraints,researchers have proposed many approaches.But when we try to follow these approaches in an interactive animation system where the object to operate on is as highly articulated as a realistic humanﬁgure,they fail in either generality or performance,and so a new approach is fostered.Our approach is based on nonlinear programming techniques.It has been used for several years in the spatial constraint system in the Jack TM humanﬁgure simulation software developed at the Computer Graphics Research Lab of the University of Pennsylvania,and proves to be satisfactorily efﬁcient,controllable,and robust.A spatial constraint in our system involves two parts:one on theﬁgure,called the end-effector,and the other one on the spatial environment,called the goal.These two parts are dealt with separately,so that a neat modular implementation is achieved.Constraints can be added one at a time with appropriate weights designating the importance of this constraint relative to the others,and the system solves them and retains them whenever a constraint is violated because either theﬁgure or the goal is moved.In case it is impossible to satisfy all the constraints thanks to physical limits,the system stops with the optimal solution for the given weights.In addition,the rigidity of each joint angle can be controlled,which is useful when degrees of freedom are redundant.Categories and Subject Descriptors:I.3.7[Computer Graphics]:Three-Dimensional Graphics and Realism–animationGeneral Terms:Algorithms,PerformanceAdditional Key Words and Phrases:Inverse kinematics,highly articulatedﬁgures,nonlinear pro-gramming1IntroductionIn computer animation,an articulatedﬁgure is often modeled as a set of rigid segments connected by joints.A joint is,abstractly,a constraint on the geometric relationship between two adjacent segments.This “relationship”is expressed by a number of parameters called joint angles.With judicious selection of joints, so that,e.g.,segments are connected to form a tree structure,a collection of the joint angles of all the joints corresponds one-on-one to a conﬁguration of theﬁgure.While this correspondence provides an immediate computer representation of articulatedﬁgure conﬁgurations in the sense that given a set of joint angles it is straightforward to compute the corresponding conﬁguration,the problem ofﬁnding a set of joint angles that corresponds to a given conﬁguration,the inverse kinematics problem,persists in practice.The inverse kinematics problem,however,is extremely important in computer animation,since it is often the spatial appearance,rather than the joint angles,that an animator is interested in.Naturally,the problem has received attention of many researchers in computer animation,as well as in robotics(see the next section),but the various algorithms reﬂect particular aspects of the problem and fail to provide a general,efﬁcient,and robust solution for positioning highly articulatedﬁgures in an interactive animation system.In interactive manipulation of articulatedﬁgures,where an animator poses aﬁgure in the spatial context whereas joint angles are merely internal(and possibly hidden)representations of postures(conﬁgurations) [18],the joint angles that deﬁne the target conﬁguration is much more interesting than the process that the joint angles take in arriving at the target.It is the responsiveness that is essential.Quick response is also essential for practical control of articulatedﬁgures where the mapping from spatial conﬁgurations to joint angles has to be done repeatedly.For example,in path planning with strength constraints,the predictionof the next conﬁguration is transformed to joint angles iteratively[14].Workspace computation is another example[1].In the former example,the time sequence is handled by some other level of control;and in the latter example,the process that the joint angles take in arriving at target postures is not pertinent.It is in this context that we offer a new approach to the inverse kinematics problem.In the following section,we shall talk about our motivation in more detail.Our approach is based on nonlinear programming, a numerical method for solving the minimum of a nonlinear function.It searches for the solution in the high-dimensional joint angle space based on computational economy rather than physical meanings.It deals with joint limits intrinsically rather than as a special case.It is successfully implemented and has found wide uses,as noted above.Because of the complex nature of nonlinear functions,many efﬁcient nonlinear programming algorithms terminate when theyﬁnd local minima.The algorithm we picked has this limitation,too.In practice, however,this is not an unacceptably serious problem.Local minima are less likely when the target conﬁguration is not too distant from the starting one.If they do occur during interactive manipulation,users can easily perturb theﬁgure conﬁguration slightly to get around the local minima.2BackgroundInverse kinematics for determining mechanism motion is a common technique in mechanical engineering, particularly in robot research[16].In robotics,however,people are mostly concerned about the functionality of manipulators;overly redundant degrees of freedom are usually not desired except for special purposes. Moreover,the computation is usually carried out on particular linkage geometries.In contrast,many interesting objects in the computer animation domain,the humanﬁgure,for example,have many redundant degrees of freedom when viewed as a tree-structured kinematic mechanism.So it was necessary to look for effective means for solving this problem under various circumstances peculiar to computer animation.Korein and Badler began to study and implement methods for kinematic chain positioning,especially in the context of joint limits and redundant degrees of freedom[12,13].In[3],Badler et al used position constraints to specify spatial conﬁgurations of articulatedﬁgures.They recursively solved for joint angles to satisfy multiple position constraints.But,owing to their simple solver,the constraints handled were limited to the type of point-to-point position constraints only.Girard and Maciejewski adopted a method from robotics.In[11],they calculated the pseudo-inverse of the Jacobian matrix which relates the increment of the joint angles to the displacement of the end-effector in space.The main formula is∆∆where∆is the increment of the joint angle vector,∆is the displacement of the vector representing the position and/or orientation of the end-effector in space,and is the pseudo-inverse of the Jacobian. To understand this,we can think of as a3-D column vector denoting the position of the hand,and as a n-D column vector consisting of all joint angles which may contribute to the motion of the hand—e.g.,all the joint angles from the shoulder to the wrist.This is a differential equality;in other words,the equality holds only if we ignore the displacement of higher order∆2.It was developed to drive the robot, where the increment is small because actual motion has to be carried out physically in continuous way.To simply position a humanﬁgure in a computer simulated environment,however,it would not be economical to move the end-effector by“small”steps;in making a computer animation sequence,it would not be optimal either to take a step size smaller than necessary.Moreover,the pseudo-inverse calculation required for each step in this formula is normally quite expensive and they did not deal with joint limits.Witkin et al used energy constraints for positioning purposes[24].Constraints can be positional or orientational.They are satisﬁed if and only if the energy function is zero.The way they solved constraints is to integrate the differential equation:where is the parameter(e.g.,joint angle)vector which deﬁnes the conﬁguration of the system,is the energy function of,and is the gradient operator.Clearly,if is the integral with some initial condition,monotonically decreases with time,because2In the joint angle space,constantdeﬁnes a line,called the iso-energy line,on which the energy function takes an identical value.For any number(energy level),there is such a line.Under this physical meaning of the energy function,Witkin et al’s method searches the path from the initial conﬁguration to the target conﬁguration which is,at any point, perpendicular to the iso-energy lines.Instead of associating energy functions with constraints,Barzel and Barr introduced deviation functions which measure the deviation of two constrained parts[5].They discussed a variety of constraints in[5],such as point-to-point,point-to-nail,etc.,and their associated deviation functions.A segment in their system of rigid bodies is subjected to both external forces,such as the gravity,and constraint forces,which bring the deviations to zero whenever they are greater.Constraint forces are solved from a set of dynamic differential equations which requires that all deviations go to zero exponentially in a certain amount of time.It is worth noting that an approach based on physical modeling and interpretation is also used by Witkin and Welch on nonrigid bodies whose deformations are controlled by a number of parameters[25].To apply this kind of methods to articulatedﬁgures,a joint would be considered as a point-to-point constraint and added to the system as an algebraic equation.This poses some practical problems that render such solutions inappropriate to highly articulatedﬁgures.First,it is not unusual to have several dozen joints in a highly articulatedﬁgure,which would add to the number of constraint equations substantially.Second,a joint of an articulatedﬁgure is meant to be an absolute constraint.In other words,it should not compete with any constraint that relates a point on a segment of theﬁgure to a point in space.This competition often gives rise to numerical instability.We notice that all those methods have a property in common:the target conﬁguration is the result of a process from a starting one.This process bears some physical meaning.In Girard and Maciejewski’s method [11],the process is determined by the end-effector path;in Witkin et al’s method[24],it is determined by the energy function(the path in space is perpendicular to the family of iso-energy lines);in Barzel and Barr’s method[5]or other dynamic methods([25]),the process is determined by the physical interpretations of each segment,and external and constraint forces exerted on it.Not only can these methods solve the constraints,but also offer a smooth process in which the constraints are satisﬁed in certain contexts.The achieved target conﬁguration is,therefore,natural in the sense that it results from a process that the user is more or less able to comprehend and control.But this property is not free.If we are only concernedabout the target conﬁguration deﬁned by the spatial constraints,rather than the physical realization,which is true in many circumstances,physical methods could be computationally inefﬁcient,because they add extra burdens to the original geometric problem.For example,in searching for a(local)minimum along a line,one mayﬁrst choose a small step size and then compute the function value until it rises.Another way toﬁnd the solution could be like this.First locate an interval in which the minimum lies,and then use the golden ratio method,a method similar to binary search,toﬁnd the minimum.Theﬁrst method shows a vivid picture of how the function changes to the minimum gradually,whereas the second method is statistically much faster.Therefore,since a target conﬁguration can be deﬁned by the minimum of an energy function(see [24]),why don’t we look for the minimum directly?As for naturalness of the target conﬁguration,we may give the user more immediate control by allowing the user to specify more constraints,if it remains affordable.Nonlinear programming is a numerical technique to solve for(local)minima of nonlinear functions. The solution search maintains numerical efﬁciency and robustness;the intermediate values from the starting state to theﬁnal one could be in general fairly“irregular”.There are two classes of nonlinear programming problems.One is the unconstrained nonlinear programming,where the variables are free to take any values; the other one is the constrained nonlinear programming,where the variables can only take values in a certain range.The constraints on the variablesﬁt exactly to joint limits of articulatedﬁgures.Although the latter problem can be theoretically reduced to the former one,both unconstrained and constrained nonlinear programming problems have been studied extensively,because simple reduction may cause numerical instability.So we propose a new approach to the inverse kinematics problem based on nonlinear programming methods.Our target application is interactive manipulation of highly articulatedﬁgures,such as human ﬁgures,where joints and joint limits must not be violated.3Spatial ConstraintsThe basic geometric entity considered here is the articulatedﬁgure.The data structure of an articulated ﬁgure we used is deﬁned by the Peabody language developed at the Computer Graphics Research Lab atcnstr.........joint angle index table weight,joint chain,θGoalG, gAssemblerMG, mgNon-linearObjective FunctionGenerator Programminggoal type,parametersEnd-effector Figure 1:Multiple Spatial Constraint Systemthe University of Pennsylvania [17].A Peabody ﬁgure is composed of rigid segments connected together by joints.Each joint has several rotational and translational degrees of freedom subject to joint limits.The data structure can be viewed as a tree,where nodes represent segments and edges represent joints.Having decided on the data structure,we need to address the problem of setting a ﬁgure to a desired posture.As discussed in the introduction,we wish to be able to adjust the posture directly in the spatial domain.Our spatial constraints are designed for this purpose.A spatial constraint is simply a demand that the end-effector on a segment of a ﬁgure be placed at and/or aligned with the goal in space.To say that a constraint is satisﬁed is equivalent to saying that the goal is reached.The end-effector’s propensity to hold on to the goal persists until the constraint is disabled or deleted.Figure 1is a diagram of the multiple spatial constraint system in Jack .The system consists of threemajor components:Objective Function Generator,Assembler,and Nonlinear Programming solver.They are described in the following sections.4End-effectors4.1End-effector MappingsFormally,we can view an end-effector as a mapping::Θ1ΘwhereΘis the joint angle space,the set consisting of all joint angle vectors,and3222 where3denotes the set of3-D vectors,and2the set of3-D unit vectors.Accordingly,is a9-D vector,whoseﬁrst three components form a positional vector,designating the spatial position of a point on the end-effector segment,the second and the third three components form two unit vectors,designating directions of two independent unit vectors on the end-effector segment.Given an instance of the joint angles of all the joints,,the end-effector associates a9-D vector according to theﬁgure deﬁnition.Since segments of aﬁgure are rigid,the angle expanded by the last two unit vectors should remain unchanged.A convenient choice is to set it to90degrees.These nine numbers uniquely determine the position and orientation of the end-effector segment in space.Theﬁrst three numbers are independent, but the next six numbers are not.They must satisfy two unity equations and one expanded angle equation. These three equations take away three degrees of freedom from,so that has only six independent quantities,which are exactly needed to determine the position and orientation of a rigid body in space.Let’s take an example.Let the end-effector segment be the right hand,and the pelvis beﬁxed temporarily, serving as the root of theﬁgure tree deﬁnition.Given joint angles of all the joints from the waist to the right wrist present in vector,the location and orientation of the right hand can be computed and the result is put in,provided that a point and two orthonormal vectors attached on the hand have been selected for reference.21 1solve the constraint requires the derivative quantities.1The matrix is the Jacobian matrix.Its use will be explained later.Naturally,it is this module’s responsibility to compute it.The vector is composed of some combination of a point vector and two unit vectors on the end-effector segment.Referring to Figure2,let be a point vector and be a unit vector on the end-effector segment.It is clear that in order to compute and,it is sufﬁcient to know how to compute, ,,and.Because all the joints in our current humanﬁgure model are rotational joints,we discuss only rotational joints here.1Let the th joint angle along the chain be,and the rotation axis of this joint be unit vector. It turns out that and can be easily computed with cascaded multiplications of4by4homogeneous matrices.The derivatives can be easily computed,too(see[26]):.(4) 5Goals5.1Goal Potential FunctionsA goal can also be viewed as a mapping::5 where the domain is the same as the range of the end-effector mapping deﬁned in(2),and is the set of non-negative real numbers.Since the function assigns a scalar to a combination of position and directions in space,we call it a potential function.When the end-effector vector is plugged into the potential function as the argument,it produces a non-negative real number,,which is to be understood asthe distance from the current end-effector location(position and/or orientation)to the associated goal.For a pair of an end-effector and a goal,the range of the end-effector must be the same as the domain of the potential function.5.2Goal Computational ModuleThe Goal module is the other part of the Objective Function Generator(Figure1).It is to compute the potential and its gradient,the column vector formed by all its partial derivatives.Let2In practice,however,it may not be adequate,because this potential function,when combined witha position goal,would in effect make one unit difference in length as important as about one radiandifference in angle,which is not always intended.To make one length unit commensurate with degrees in angle,we need to multiply the above by a factor such that1360or,explicitly3602.8 To be moreﬂexible,the potential function is chosen to be2222.9 The gradient is then22(10)22.(11)A goal direction,such as,could be unconstrained by setting to0.This is useful,for example,to orientationally constrain the normal to the palm of a person holding a cup of water.Position/Orientation Goals.The position and orientation goal can be treated as two goals,but some-times it is more convenient to combine them together as one goal.The potential function for the position/orientation goal is chosen to be a weighted sum of the position and orientation components:2222212 where and are weights assigned to position and orientation,respectively,such that1.The domain322and the gradients,and can be calculated from(7),(10),and(11)above.Aiming-at Goals.The goal is deﬁned by a point in space;the end-effector is deﬁned by a position vector and a unit vector on the end-effector segment.The goal is reached if and only if the ray emanating from in the direction passes through.The domain of the potential function32This type of goal is useful,for example,in posing a humanﬁgure facing toward a certain point.The potential function2.(15)Line Goals.The goal is deﬁned by a line which passes through points and,where is a unit vector.This line is meant for a point on the end-effector segment to lie on.The potential function2;16its domain3and gradient2.17Plane Goals.The goal is deﬁned by a plane with the unit normal to and a point on it.Similar to the Line Goal,the plane is meant for a point on the end-effector segment to lie on.The potential function2;18its domain3and the gradient2.19 Half-space Goals.The goal is deﬁned by a plane speciﬁed the same way as in the Plane Goal.The plane is used to divide the space into two halves.A point on the end-effector segment“reaches”the goal if and only if it is in the same half-space as the point is.The potential function0if0;202otherwiseits domain3and the gradient0if0212otherwise.6Spatial Constraint as a Nonlinear Programming ProblemA spatial constraint constrains an end-effector to a goal.From Section4and5,with the current joint angles being,the“distance”from the end-effector to the goal is simply22 This quantity can be computed byﬁrst invoking the end-effector module to compute,and then invoking the goal module with as the input argument of the potential function.This process is illustrated in Figure1.Ideally,we want to solve the algebraic equation,In reality,however,this equation is not always satisﬁable,for the goal is not always reachable.Thus the problem would be naturally toﬁnd in a feasible region that minimizes the function.Most of the joint angles in ourﬁgure deﬁnition have lower limits and upper limits.The joint angles for the shoulderare conﬁned in a polygon.They can all be expressed in linear inequalities.Therefore,we formulate the problem as a problem of nonlinear programming subject to linear constraints on variables,that is,formally,minimize23subject to1212where12are column vectors whose dimensions are the same as that of’s.The equalities allow for linear relationships among the joint angles,and the inequalities admit of the lower limit and upper limit on,the th joint angle,as do the inequalities.The polygonal region for the shoulder joint angles(elevation,abduction,and twist)can be similarly expressed as a set of inequalities.7Solving the Nonlinear Programming ProblemThe problem posed in(23)toﬁnd the minimum of the objective function is intractable without knowledge of the regularity of the objective function.Properties such as linearity or convexity that regulate the global behavior of a function may help toﬁnd the global minimum.Otherwise,research in nonlinear programming area is mostly done to solve for local minima.It is worthwhile because,in practice,functions are moderate:the local minimum is often what one wants,or if it fails to be,some other local minimum found by another attempt with a new initial point would quite likely be.In order to have quick response,we chose to compromise for local minima.From years of observation, we have not seen many serious problems.The algorithm we used to solve the problem(23)is described in the Appendix.It iterates to approach the solution.At each iteration,it searches for a minimum along a certain direction.In order for the search direction to point to the solution more accurately so that fewer iterations will be needed,the direction is determined based on not only the gradient at the current point,but also the gradients at the previous steps of iteration.Our method is monotonic,namely that after any iterations the value that the objective function takes never increases,and globally convergent,namely that it converges to a(local)minimum regardless of the initial point.These two properties are very attractive to us because the conﬁguration could otherwise diverge arbitrarily,which could cause disaster had the previous posture resulted from substantial effort.To carry out the computation,we need to compute and its gradient.It becomes easy now after preparation in Sections4and5.The function value can be computed as in(22),and the gradient can be computed as follows:defTherefore,our system handles multiple constraints.Since the objective function deﬁned in(22)is non-negative,the multiple constraints are solved by minimizingthe sum of the objective functions associated with all the goalsall251where is the number of constraints,subscript denotes the association with the th constraint,is a non-negative weight assigned to the th constraint to reﬂect the relative importance of the constraint,and26 Thus,the multiple constraints can be solved as the problem(23)with replaced by all deﬁned in (25).Note that’s can be computed independently,and only a number of additions are needed to compute all.This is also true for the gradient,for the gradient operator is additive,too.Constraints may also be tied together disjunctively,that is,they are considered satisﬁed if any one of them is satisﬁed.To solve this problem,we deﬁne the objective function asall min271It is useful,for example,to constrain an end-effector outside a convex polyhedron,because the outside space can be viewed as the disjunction of the outward half-spaces deﬁned by the polygonal faces.9Assembler of Multiple ConstraintsAs stated in the previous sections,the overall objective function of multiple constraints can be found by computing separately and independently the objective functions of individual constraints and then adding them together.In this section,we shall explain how the Assembler works.The module Objective Function Generator takes a joint chain,an array of corresponding joint angles, goal type,and other parameters of a constraint as its input and computes the objective function value and its gradient.Since the partial derivatives with respect to the joint angles other than those on the joint chain are zero,the gradient determined by this module has to include only the derivatives with respect to the joint angles on the chain.This property lends itself to a clean modular implementation.However,two gradientvectors so structured for different constraints do not add directly—the th joint angle in one chain may not be the same as the th joint angle in another chain.The difference is resolved by the Assembler module.Suppose there are constraints.LetΘbe the ordered set of joint angles on the joint chain of the th constraint,and be the number of joint angles inΘ.LetΘ1Θ28 the union of allΘ’s with the order deﬁned in certain way,and be the number of joint angles inΘ.In general,1,because of possible overlap amongΘ’s.Let’s deﬁne the index table as a mapping:121229 such that the th joint angle inΘcorresponds to the th joint angle in the overall index systemΘ.This index table,along with the weight of the constraint,are passed to the Assembler so that the effect of the th constraint to the gradient of the overall objective function all can be correctly accounted.Once the’s, the derivative of the objective function of the th constraint with regard to the th joint angle inΘ,are available,the Assembler does:For1to do,for12,where stands for the partial derivative of all with regard to the th joint angle inΘ.They are initially set to zero.10Reconciliation of Joint ChainsIt was suggested in Expression(28)that only a union was needed to combine all the joint chains.In fact,it is slightly more complicated,because we allow the user to specify the set of joints in the joint chain as the resource for the constraint satisfaction.The joint chain does not have to go from the end-effector segment back to the root in theﬁgure deﬁnition,and is speciﬁed by the user when he or she deﬁnes the constraint. Since the constraints may be input one by one,a joint which may affect the end-effector of one constraint but is not picked for the joint chain could well be picked for the joint chain of another constraint.For。

老高考适用2024高考英语一轮总复习第一编教材回眸Unit5Rhythm北师大版

Unit 5 Rhythm晨起第一事背诵经典句1．Listening to music is one of the most common ways we manage our stress and emotions.听音乐是我们应对压力和调整心情的最常用方式之一。

2．As an old saying goes, “music is universal.”常言道：“音乐无国界”。

3．In a word, not only his talents in music but also his appearance left a deep impression on me.总之，不仅他的音乐才华，他的外表也给我留下了深刻的印象。

4．Music has a kind of charm, which can inspire people to be kind, and can also tempt people to go on the path of degeneration.音乐有一种魔力，可以感化人心向善，也可以迷人走上堕落之路。

Ⅰ核心单词(1)effect (n.) 效果，作用→effective (adj.) 有效的→effectively (adv.) 有效地(2)disappoint (vt.) 使悲观→disappointed (adj.) 感到悲观的→disappointing (adj.) 令人悲观的→disappointment (n.) 悲观(3)unclear (adj.) 不清晰的→unclearly (adv.) 不清晰地(4)performance (n.) 表演；演奏→perform (vi.) 表演，表现；履行，完成→performer (n.) 表演者(5)award (n.) 奖，奖品 (vt.) 颁发，授予(6)extremely (adv.) 极端地；特别地→extreme (adj.) 极端的，偏激的→extremeness (n.) 极端，极度→extremism (n.) 极端性(7)creative (adj.) 有创建力的，创建性的→create (vt.) 创建，独创→creation (n.) 独创，创建→creatively (adv.) 具有创建性地(8)powerful (adj.) 强大的，有力的→power (n.) 权力，势力→powerfully (adv.) 剧烈地；强有力地(9)anger (n.) 生气，生气→angry (adj.) 生气的，生气的→angrily (adv.) 生气地，生气地(10)audience (n.) 观众，听众(11)throughout (prep.) 贯穿，遍及(12)impress (vt.) 使(人)印象深刻→impression (n.) 印象→impressive (adj.) 给人深刻印象的，感人的→impressively (adv.) 令人难忘地→impressiveness (n.) 令人难忘(13)instrument (n.) 乐器；工具→instrumental (adj.) 用乐器演奏的→instrumentally (adv.) 用乐器演奏地(14)treasure (n.) 财宝，财宝(15)combine (vt.) (使)结合，(使)联合→combination (n.) 结合；团体；联合→combined (adj.) 结合的(16)represent (vt.) 代表→representation (n.) 代表，代理，表现→representative (adj.) 典型的，有代表性的(17)key (n.) 琴键；答案；关键；钥匙(18)talent (n.) 天才，才能→talented (adj.) 有天资的，有才能的(19)identity (n.) 身份，特征→identify (vt.) 认出；识别；鉴定(20)appearance (n.) 外观，外貌；出现→appear (vi.) 出现，看起来似乎，似乎(21)transform (vt.) 转换，转变，转化→transformation (n.) 转换，转化(22)ordinary (adj.) 平常的，一般的→ordinarily (adv.) 通常地；一般地(23)generation (n.) 代，一代(24)unique (adj.) 独特的，唯一的→uniquely (adv.) 独特地，唯一地→uniqueness (n.) 唯一性，独特(25)responsible (adj.) 有责任的，肩负责任的→response (n.) 反应，响应→responsibly (adv.) 可以信任地；牢靠地→responsibility (n.) 责任，职责(26)permission (n.) 允许，许可→permit (vt.) 许可，允许Ⅱ阅读单词(1)folk (adj.) 民间的 (n.) 家属；人们(2)extraordinary (adj.) 非凡的，特殊的→extraordinarily (adv.) 特别地(3)album (n.) 唱片；相册；集邮册(4)fan (n.) 热心的追随者(5)base (n.) 基地，基础→based (adj.) (以某事)为基础；基地在……→basic (adj.) 基本的→basically (adv.) 基本上；总的说来→basis (n.) 基准，准则；方式；缘由；基础(6)system (n.) 系统；制度；体制(7)male (adj.) 男性的，男性(8)carriage (n.) 马车(9)quit (vt.& vi.) 停止；辞职(10)rediscover (vt.) 重新发觉(11)type (n.) 类型，种类(12)skip (vi.) 跳，蹦 (vt.) 跳过(13)noble (adj.) 高尚的，名贵的，贵族的→nobility (n.) 高尚，贵族→nobly (adv.) 名贵地；崇高地(14)immigrant (adj.) 移民的，移居的→immigrate (vt.) 移居，移入→immigration (n.) 移民(15)reaction (n.) 反应→react (vi.) 反应→reactive (adj.) 能起反应的，活性的[单句语法填空]1.The design of the bicycle has managed to reduce the (effect) of wind resistance and drag.答案：effects2．I am sorry, but in fact I'm rather (clear) about what I'm supposed to be doing here.答案：unclear3．His words at the meeting that day (impress) on my memory strongly.答案：were impressed4．I was very (anger) with myself for making such a stupid mistake.答案：angry5．She's very (create)—she writes poems and paints.答案：creative6．The firm is working on a new product in (combine) with several overseas partners.答案：combination7．It's a device which (identify) its owner through his fingerprint pattern.答案：identifies8．We are often attracted to somebody first by their physical (appear)．答案：appearance9．It was an event that (transform) my life.答案：would transform10．No official (permit) has been given for the event to take place.答案：permissionn．＋ful构成的形容词①powerful 有力的，有权力的②wonderful 奇妙的，精彩的③helpful 有帮助的④useful 有用的⑤meaningful 有意义的⑥thankful 感谢的⑦grateful 感谢的⑧careful 细致的⑨colorful 充溢色调的⑩regretful 缺憾的⑪hopeful 有希望的⑫fearful 胆怯的⑬beautiful 漂亮的⑭thoughtful 周到的⑮respectful 表示敬重的，敬重人的⑯forgetful 健忘的⑰delightful 令人兴奋的⑱frightful 可怕的⑲painful 令人苦痛的⑳harmful 有害的1．be used/accustomed to (doing) sth习惯于(做)某事2．come out 出版，发行3．warm up 热身，使更活跃4．react to 对……做出反应5．be filled with 充溢6．be impressed with/by 对……留下深刻印象7．play an important role in 在……中扮演重要角色8．in other words 换句话说9．combine ... with 将……与……合并/结合10．at times 有时；间或11．in some ways 在某些方面12．be expected to 有望，希望；预料13．back and forth 反复来回14．refer to 描述，涉及；查阅15．be responsible for 对……负有责任[选词填空]be used to, come out, be full of, be impressed with, in other words, combine ...with, be expected to, refer to, be responsible for, back and forth1．There are ferries sailing between the islands.答案：back and forth2．The music we hear now is the product of traditional Chinese style Western style.答案：combining; with3．The teacher in my last letter has gone abroad.答案：referred to4．We felt at home with her and the depth of her knowledge.答案：were impressed with5．The talks continue until tomorrow.答案：are expected to6．I the matter. None of others' business.答案：am responsible for7．They asked him to leave—， he was fired.答案：in other words8．The rest of the cast her being the centre of attention.答案：was used to9．Her third album last month.答案：came out10．He anxiety all the time.答案：is full of1．与back and forth结构相像的短语①sooner or later 迟早②up and down 来回；往复③in and out 进进出出④here and there 到处⑤more or less 或多或少⑥do's and don'ts 留意事项⑦home and abroad 国内外⑧come and go 来往；自由走动⑨black and white 白纸黑字；黑白⑩right or wrong 不管对错⑪far and near 到处，四面八方⑫young and old 老老少少⑬day and night 日日夜夜⑭rain or shine 不论晴雨；无论如何⑮rights and wrongs 是非曲直⑯ups and downs 沉浮⑰black and blue 体无完肤2．与time构成的短语①in time 刚好，按时；迟早②time and again 多次③against time 争分夺秒，赶时间④at a ti me 一次；一度⑤for the time being 短暂，目前，眼下⑥from time to time 有时⑦all the time 始终，始终⑧at the same time 同时⑨on time 准时⑩the whole time 自始至终⑪many a time 多次⑫keep time 合拍子；(钟表)走得准⑬in no time 马上，立刻⑭behind the times 落在时代后面，过时⑮at times 有时，间或课文原句句式梳理仿写训练1.What about your grandpa and grandma? Who's going to help me look after them if you go？你爷爷奶奶怎么办？假如你去，谁来帮我照看他们？(P25) What about ... ？＝Howabout ...？“……怎么样？”本句型常用于征求看法，about后跟名词、代词或动名词作介词宾语for anouting this weekend？本周末外出郊游好吗？2.Would it be all right ifI missed the English test next week？假如我下星期不参与英语考试好吗？(P25) 句型“主语＋would＋v.＋其他＋if＋主语＋动词的过去式＋将来时间状语”是对将来发生的动作的假设If ittomorrow, wethe sports meeting.假如明天下雨的话，我们就得推迟运动会。

机械类外文文献翻译机械类英文翻译机械专业毕业设计中英文翻译机械专业中英文翻译机械专业英文翻译(优.选)

中英文翻译原文：Comment on medicines and chemical reagents package machineryconceptual designIn recent years, Carry out GMP (medicines and chemical reagents produces specifications of quality) attestation system because of sustained our country economic situation rise and country to pharmacy industry mandatory. Medicines and chemical reagents package machinery has got quite great progress. The new product increases by gradually. Engineering level has had very big improvement. But be returning very big gaps back to existence compared with international standards. Level being close to 60%'s product cannot to reach upper developed country century eighties. Large-scale advanced equipment is dependent on entrance mainly. Low our country medicines and chemical reagents package machinery engineering level is that the design designing personnel low level from our country enterprise arouses to a great extent.One, our country medicines and chemical reagents package machinery current situation analysesOur country medicines and chemical reagents package machinery still has bigger gap compared with advanced international level. What time is insufficient on domestic medicines and chemical reagents package machinery design under main existence1) Backward domestic mechanical performance medicines and chemical reagents package machinery mostly, accuracy low velocity, is slow, stationarity dispatches package machinery travel process to contain large amount of dyadic complicated intermittence motion. Come to come true mainly from the cam, the connecting rod. But, many design that the personnel is unable to require that the independence designs the parameter calculating cam bar linkage kinematics and dynamics according to job cycle picture and accuracy. Be only the surveying and mapping carrying out a piecemeal that the abroad model machine cam connecting rod part is dismantled down simplely. Bring about actuating mechanism error is very big. That domestic medicines and chemical reagents package machinery runs speed mostly is more general than hanging down according to cutting frequency if the aluminium moulds bubble coverpacker's for 100 one 300 mins, full-automatic medicine box packer dress box speed 50- 200 boxes/ ms in. But, on the international, the advanced aluminium moulds rushing steeping cover packer cutting frequency be able to reach 600 mins. Full-automatic medicine box packer dress box speed is able to reach 600 ~ 800 box/ mins. Not only working speed of domestic medicines and chemical reagents package machinery is slow. And, the partner has bigger noise.2) Is under the control of horizontal backward. Domestic medicines and chemical reagents package machinery controls low, automation of level difference mostly , the malfunction leads height. (Main package machinery finger box dress controls domestic medicines and chemical reagents with drinking wine holding machinery with) adopt PLC to do a scene mostly. But, advanced medicines and chemical reagents package machinery realizes supervisory control abroad mostly from computer system. Under the control of horizontal relatively backward. Great majority domestic medicines and chemical reagents package machinery automation sex is relatively poor. Adopt a single to produce a pattern first commonly. The full-automatic production line is few. Two is that full-automation works cannot to achieve. Require that the manpower feeds in raw material. Hand movement enchases. If in a little paper box packer, Page, paper box all needs medicine board , specifications paper to move charging personally. And require specially-assigned person to pay attention to if specifications, medicine board, paper box already finish using at any time. Happen to avoid bringing about machine racing or bringing about incomplete specifications, medicine board, and medicine box phenomenon. Other, domestic medicines and chemical reagents package mechanic failure rates are higher. Control a component (if the relay, electromagnetic valve, contactor, breaker etc.) etc. are often easy to damage. Halt also to frequently occur the malfunction.3) Functions are unitary, expansion sex is bad. Medicines and chemical reagents package machinery is that the form designs that specifically for specially appointed package. The general specification range inner in regulation is adjustable. But, a lot of our country medicines and chemical reagents package machinery considers insufficiency when designing that. Be not that reforming going a step further sets apart sufficient space. Cause the machinery designing that to be able to only adapt to the form board in several kinds simplicities. Change not adapting to wrapping material or the form board dimension. Fit in with even. The package finished product mass giving birth to a child is neither nice.4) Considers deficiency synthetically. Resource does not fully utilize. Our country medicines and chemical reagents there exists the chaos phenomenon in package machinery design. A lot of machinery designs that the personnel drags to the electric motor moving the synchrony technology, the servo drive technology do not knows. The problem simple electrical equipment available is resolved uses complicated mechanism to come to come true but. Some though the control organ works to come having adopt the synchrony electric motor to wait for a device. But choose block of wood ding-dang. The maximum having brought about resource not only wastes this condition. And make machinery function designing that low.5) Model is inflexible. Model seldom considering machinery time medicines and chemical reagents of our country package machinery design. Many machine molding that the manufacturer produces is not beautiful do not have model even. Give person feeling to rigid, to inflexible, not to have vigor. A few medicine box packers are middle. The nut all assembles screw on the machine outside board. But, the oil cup and flow nipple that a little lubrication uses also can be seen everywhere. Be stained fully with a greasy dirt easy to use machine everywhere time oiling. Impression is rough to person. No beautiful.Two, medicines and chemical reagents package machinery conceptual design contentPeople long-term study passes. Define conceptual design being: "Have been ascertaining the mission queen. Pass abstract-relation. Design the function structure. Explore appropriate effect principle and their combination waiting. Ascertain out basic finding the solution approach. Reach find the solution scheme. This part of the conceptual design designing that the job is called conceptual design is referred to make the queen who designs purpose and now has condition clear. The designer searches for many-sided knowledge. Analysis abstracts the solution on generating dyadic broad frame significance the day after tomorrow. Medicines and chemical reagents package machinery conceptual design demands according to each product life cycle stages. Carrying out the product function creates , the function breaks up as well as the function and son are functional physical design: That conception and systematization carrying out the scheme satisfying the operating principle that the function and structure demand finding the solution and carrying out the operating principle carrier realizing the function structure's design the conceptual design process is that one finds the solution realizing a function's , satisfies the various technologyand various there existing in economic target's , possibility scheme well ultimate for sure synthetically optimum scheme process. The conceptual design effect embodies in the product design early phase stage mainly. Chief architect is based on functional need of product but primitive conception and impulsion sprouting out form the product main body frame. And, it responds to every main module and module including. In order to accomplishing overall layout and the exterior, the first step designs that. And then carry out the optimization appraising a sum. Ascertain the overall design plan. Design that the personnel carries out the chief architect design thought going to designing middle concretely again from every part. Detail designs realization. The conceptual design putting medicines and chemical reagents package machinery into practice demands to design that the personnel reinforces the cognition to medicines and chemical reagents package first. Deepen the connotation understanding medicines and chemical reagents packages. Introduce modern package idea. Be in line with the international conventions actively. Modern package is to ensure the product safety not only. Make product transportation convenient. And be getting up propagate, environmental protection, defends against false. Attractive looks waits for the many-sided effect. Wrap up contents additional information. The medicines and chemical reagents package machinery design personnel should show solicitude for development of package system closely. Go deep into the handicraft studying package. Know demand of development of wrapping material and the person to machinery product very well. Only when such ability designs that out satisfy the high tone machinery product that the consumer demands. Medicines and chemical reagents package machinery conceptual design content has mainly:1) Makes the design mission clear. Be ready for feasibility analysis. The designer designs initial stage working in being in progress. Respond to the feasibility considering a product sufficiently. One aspect is the marketplace thinking. Include the production marketing, product raw material, the fabricating cost thinking: Another aspect is thinking that the product processes. Include thinking now having a working ability, processing handicraft, processing the function and periphery supporting industry. Periphery supporting environment thinking points to the local enterprise working ability mainly processes level, heat treatment handicraft and the infrastructural facilities construction etc.2) Function design. Great majority our country medicines and chemical reagents package machinery is the same kind model copying to abroad. But peculiar nationalconditions because of our country existence. Must carry out appropriate reforming on the product. To satisfy request of our country. But fault blindly copy blindly. The machinery designing that is packed in, irrigates the dress function outside except needing to satisfy a box. We must consider the additional function packing machinery. If in package box should add a counting cup. The medicine spoon waits an utensil down. Be put into use with convenience of customers. In machine, kind of aspect developing can design comparatively advanced machinery. If sterile pack machinery, the package machinery retaining freshness etc.Can develop the corollary equipment selling complete sets of equipment and the post-processing at reduced prices in the medicines and chemical reagents package front.3) Functions decomposition. Medicines and chemical reagents package machinery belongs to the integration of machinery with electronics product. Should consider every function all round time design. Sort Er Yan. The medicines and chemical reagents package machinery function may divide 3 major parts being that organization moves, monitors biography feel, the information processing and controlling a function basically. The function subdivides organization motion according to may not kind with machine , packer may be molding , heat-seal , pressure trace mark, according to cutting 4 big functions if the aluminum moulds bubble cover. But, paper box package machinery may be that the box opens, paper box transfers, breaks tongue , functions such as inserting tongue , flattening and putting a batch number up mark poison board under paper folding, deducing paper feed. Want to consider machinery lubrication, safe functions such as running, packing hygiene of machinery too in the process of design. This demands the technology designing that the personnel considers detecting sufficiently. Brightness, machine, electricity integration technology, computer art. Intersection between the pneumatic technology, the logistics technology connection.4) Organization is designed. Be to realize the predetermined function. We need to use different organization. This needs the part synthesizing each considering a complete machine among one process. Use the product designing that while satisfying the usage request. Structure is simple, pragmatic. Medicines and chemical reagents package machinery organization designs time. Respond to the principle choosing appropriate organization motion and constituting. Think sufficiently to realize what specially appointed motion needs organization. If cam organization. Bar linkage. Cam bar linkage. Respond to the technology wielding separation drive at the same time.Think that the transmission shaft designs a problem (if castellated shaft and ladder axis etc.) and drive are systematic synthetically. Design that process middle should cut down the effect that the uncertainty factor brings about to the full. Messenger organization operation is stable. Design that machinery carries out kinetic methods of analysis answering now and then. With lifting, machinery runs speed and stationarity. Should think that various packing machinery, adjustable, holds the mistake, but expansion, stationarity as well as beautiful-rization besides. Run after machinery is deft but stable. Design process but consult package machinery design of all kinds strong point. Draw other machinery (if plastic machinery, prints machinery) merit at the same time. Design the outside except carrying out organization. Return approach back to the realization should think that every function is other. If vacuum, electrical equipment waits under the control of. To expect that optimum combination is a product's turn.5) System under the control of schemes design. In medicines and chemical reagents package machinery, a very important part is that real time detecting is back-off to every organization. To ensure that equipment operation is smooth. Now many machinery products has selected and used large amount of photo electricity switch being the detecting component. Equipment has such as PC detecting bubble cover system on some machinery and the like system. This need all designs that meticulously. And, the general naval company is an integral whole.Three, concluding remarksThe thought a concept is designed melts to enter medicines and chemical reagents package machinery design being able to fall off designing a fault. Shorten a design cycle. Accelerate the product exploitation. Make the product designing that more rational, have affinity, more suitable man-machine project more. It is also that the main means costing down and improving enterprise competition is short of passive competition aspect backward for improving medicines and chemical reagents package machinery design at the same time. To adapt to the challenge that "queen GMP times" brings about. Design that the personnel must take product conceptual design seriously. Deepen the significance understanding conceptual design's.译文论药品包装机械的概念设计近年来，由于我国经济形势的持续高涨和国家对制药行业强制性推行GMP(药品生产质量规范)认证制度，药品包装机械取得了长足的进步。

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Experiment2Back and Forth MotionLots of objects go back and forth; that is, they move along a line first in one direction, then move back the other way. An oscillating pendulum or a ball tossed vertically into the air are examplesof things that go back and forth. Graphs of the position vs. time and velocity vs. time for suchobjects share a number of features. In this experiment, you will observe a number of objects that change speed and direction as they go back and forth. Analyzing and comparing graphs of their motion will help you to apply ideas of kinematics more clearly.In this experiment you will use a Motion Detector to observe the back and forth motion of the following five objects:•Oscillating pendulum•Dynamics cart rolling up and down an incline•Student jumping into the air•Mass oscillating at the end of a spring•Ball tossed into the airOBJECTIVES•Qualitatively analyze the motion of objects that move back and forth.•Analyze and interpret back and forth motion in kinematics graphs.•Use kinematic graphs to catalog objects that exhibit similar motion.MATERIALScomputer incline with dynamics cartVernier computer interface rubber ball (15 cm diameter or more)Logger Pro protective wire basket for Motion DetectorVernier Motion Detector protractorpendulum with large bob meter stickspring with hanging massPRELIMINARY QUESTIONS1. Do any of the five objects listed above move in similar ways? If so, which ones? What dothey have in common?2. What is the shape of a velocity vs. time graph for any object that has a constant acceleration?3. Do you think that any of the five objects has a constant acceleration? If so, which one(s)?4. Consider a ball thrown straight upward. It moves up, changes direction, and falls back down.What is the acceleration of a ball on the way up? What is the acceleration when it reaches itstop point? What is the acceleration on the way down?Experiment 2PROCEDUREThese five activities will ask you to predict the appearance of graphs of position vs. time and velocity vs. time for various motions, and then collect the corresponding data. The Motion Detector defines the origin of a coordinate system extending perpendicularly from the front of the Motion Detector. Use this coordinate system in making your sketches. After collecting data with the Motion Detector, you may want to print the computer graphs for use later in the analysis.Part I Oscillating Pendulum1. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface.Motion DetectorFigure 12. Open the file “02 Pendulum” from the Physics with Computers folder.3. Sketch your prediction of the position vs. time and velocity vs. time graphs of a pendulumbob swinging back and forth. Ignore the small vertical motion of the bob and measureposition along a horizontal line in the plane of the bob’s motion. Based on the shape of your velocity graph, do you expect the acceleration to be constant or changing? Why? Will itchange direction? Will there be a point where the acceleration is zero?4. Place the Motion Detector near a pendulum with a length of 1 to 2 m. The Motion Detectorshould be level with the pendulum bob and about 1 m away when the pendulum hangs at rest.The bob should never be closer to the detector than 0.4 m.5. Pull the pendulum about 15 cm toward the Motion Detector and release it to start thependulum swinging.6. Click to begin data collection.7. If you do not see a smooth graph, the pendulum was most likely not in the beam of theMotion Detector. Adjust the aim and repeat Steps 5 – 6.8. Answer the Analysis questions for this Part I before proceeding to Part II.Part II Dynamics Cart on an Incline9. Open the experiment file “02 Cart.” Two graphs will appear on the screen.10. Place the Motion Detector at the top of an incline that is between 1 and 2 m long. The angleof the incline should be between 5° and 10°.11. Sketch your prediction of the position vs. time and velocity vs. time graphs for a cart rollingfreely up an incline and then back down. The cart will be rolling up the incline and toward the Motion Detector initially. Will the acceleration be constant? Will it change direction?Will there be a point where the acceleration is zero?Back and Forth Motion 12. Hold the dynamics cart at the base of the incline. Click to begin taking data. Whenyou hear the clicking, give the cart a push up the incline. Make sure that the cart does not get closer than 0.4 m to the Motion Detector and keep your hands away from the track as the cart rolls.13. Zoom in on the portion of each graph that represents the time that the cart was freely rolling.To do this, use the mouse to drag a rectangle around the useful portion of the data, then click the Zoom In button, . Answer the Analysis questions for Part II before proceeding toPart III.Part III Student Jumping in the Air14. Open th e experiment file “02 Jump.”15. Secure the Motion Detector at least 3 m above the floor, pointing down.16. Sketch your predictions for the position vs. time and velocity vs. time graphs for a studentjumping straight up and falling back down. Will the acceleration be constant? Will it change direction? Will there be a point where the acceleration is zero?17. Stand directly under the Motion Detector.18. Click to begin taking data. When you hear the clicking, bend your knees and jump.Keep your arms still while in the air.19. Zoom in on the portion of the graph representing the jump. Include everything from thebending of the knees to the landing. To do this, use the mouse to drag a rectangle around the useful portion of the data and click the Zoom In button, . Answer the Analysis questionsfor Part III before proceeding to Part IV.Part IV A Mass Oscillating at the End of a Spring20. Open the experiment file “02 Spring.”21. Place the Motion Detector so it is facing upward, about 1 m below a mass suspended from aspring.22. Sketch your prediction for the position vs. time and velocity vs. time graphs of a masshanging from a spring as the mass moves up and down. Will the acceleration be constant?Will it change direction? Will there be a point where the acceleration is zero?23. Lift the mass about 10 cm (and no more) and let it fall so that it moves up and down.24. Click to begin data collection.25. If you do not see a smooth graph, the mass most likely was not in the beam of the MotionDetector. Adjust the aim or look for interfering objects and try again.26. Zoom in on the portion of each graph that represents one cycle of the mass. To do this, usethe mouse to drag a rectangle around the useful portion of the data and click the Zoom Inbutton, . Answer the Analysis questions for Part IV before proceeding to Part V.Experiment 2Part V Ball Tossed into the AirMotion DetectorFigure 227. Open the experiment file “02 Ball.”28. Sketch your predictions for the position vs. time and velocity vs. time graphs of a ball thrownstraight up into the air. Will the acceleration be constant? Will it change direction? Will there be a point where the acceleration is zero?29. Place the Motion Detector on the floor pointing toward the ceiling as shown in Figure 2.Place a protective wire basket over the Motion Detector.30. Hold the rubber ball in the palm of your hand, about 0.5 m above the Motion Detector.31. Click to begin data collection.32. When you hear the Motion Detector clicking, gently toss the ball straight up over the MotionDetector. Move your hands quickly out of the way so that the Motion Detector tracks the ball rather than your hand. Catch the ball just before it reaches the wire basket.33. Zoom in on the portion of each graph that represents the time that the ball was in the air. Todo this, use the mouse to drag a rectangle around the useful portion of the data and click the Zoom In button, .Back and Forth MotionANALYSISPart I Oscillating Pendulum1. Print or sketch the position and velocity graphs for one oscillation of the pendulum. Comparethese to your predicted graphs and comment on any differences.2. Was the acceleration constant or changing? How can you tell?3. Was there any point in the motion where the velocity was zero? Explain.4. Was there any point in the motion where the acceleration was zero? Explain.5. Where was the pendulum bob when the acceleration was greatest?6. Return to the procedure and complete the next part.Part II Dynamics Cart on an Incline7. Print or sketch the portion of the position and velocity graphs that represent the time that thecart was going up and down the incline. Compare these to your predicted graphs andcomment on any differences.8. Was the acceleration constant or changing? How can you tell?9. Logger Pro can display the tangent line to a curve, as well as display the slope numerically.To turn on this function, click on the tangent button, . Use the tangent line and the velocity graph to determine the acceleration of the cart when it was on the way up, at the top, and on the way down the incline. What did you discover?10. Was there any point in the motion where the velocity was zero? Explain.11. Was there any point in the motion where the acceleration was zero? Explain.12. Return to the procedure and complete the next part.Part III Student Jumping in the Air13. Print or sketch the portion of the position and velocity graphs that represent the time from thefirst bend of the knees through the landing. Compare these to your predicted graphs andcomment on any differences.14. Use the Tangent Line button, , to determine where the acceleration was greatest. Was itwhen the student was pushing off the floor, in the air, or during the landing?15. When the student was airborne, was the acceleration constant or changing? How can you tell?16. Was there any point in the motion where the velocity was zero? Explain.17. Was there any point in the motion where the acceleration was zero? Explain.18. Return to the procedure and complete the next part.Part IV Mass Oscillating on a Spring19. Print or sketch the position and velocity graphs for one vibration of the mass. Compare theseto your predicted graphs and comment on any differences.20. Was the acceleration constant or changing? How can you tell?Experiment 221. Was there any point in the motion where the velocity was zero? Explain.22. Was there any point in the motion where the acceleration was zero? Explain.23. Where was the mass when the acceleration was greatest?24. How does the motion of the oscillating spring compare to the pendulum?Part V Ball Tossed into the Air25. Print or sketch the portion of the position and velocity graphs that represent the time the ballwas in the air. Compare these to your predicted graphs and comment on any differences.26. Was the acceleration constant or changing? How can you tell?27. Use the tangent line and the velocity graph to determine the acceleration of the ball when itwas on the way up, at the top, and on the way down. What did you discover?28. Was there any point in the motion where the velocity was zero? Explain.29. Was there any point in the motion where the acceleration was zero? Explain.Analysis of all Parts30. State two features that the five position graphs had in common. State two ways that the fiveposition graphs were different from one another.31. State two features that the five velocity graphs had in common.32. State two ways that the five velocity graphs were different from one another. EXTENSIONS1. Investigate other back-and-forth motions such as:•Bouncing balls•A dynamics cart with a plunger bouncing off a solid object•A yo-yo2. Attach an accelerometer to your belt and use it to analyze your motion when you jump up.Compare your landing acceleration when you bend your knees upon impact and when you do not bend your knees. Safety warning: Jump only a few inches when you do not bend your knees.3. Use a force sensor to measure the force in the vibrating spring and relate this to the kinematicgraphs that you observed in this experiment.。

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