当前位置：文档之家 › KINEMATICS AND DYNAMICS OF AN OMNIDIRECTIONAL MOBILE PLATFORM WITH POWERED CASTER WHEELS Ab

KINEMATICS AND DYNAMICS OF AN OMNIDIRECTIONAL MOBILE PLATFORM WITH POWERED CASTER WHEELS Ab

  • 格式：pdf
  • 大小：1.21 MB
  • 文档页数：10

下载文档原格式

  / 10

合集下载

全向轮

全向轮

(7) 其中下标 1～4 分别代表四个轮子 ,如图 4.
3 自由方向轮系( Free2directional wheels)
3. 1 Swedish 轮
Swedish 轮也称 Mecanum 轮 ,由轮辐和固定在
外周的许多小滚子构成 ,轮子和滚子之间的夹角为 γ,通常夹角 γ为 45°,如图 3 所示[2 ] .
第 25 卷第 5 期 2003 年 9 月 文章编号 : 100220446 (2003) 0520394205
机器人 ROBOT
Vol. 25 ,No. 5 Sept . ,2003
全方位移动机器人结构和运动分析 Ξ
赵冬斌 , 易建强 , 邓旭
(中国科学院自动化研究所 复杂系统与智能科学实验室 , 北京 100080)
连续切换轮的基础为 Transwheel 轮 ,由一个轮 盘和固定在轮盘外周的滚子构成. 轮盘轴心同滚子
3 95
由世界坐标系转换为机器人坐标系的矩阵为
cosθ sinθ 0
R (θ) = - sinθ cosθ 0
(1)
0
01
文献[ 1 ]将轮子划分为传统轮系 ,包括固定方向
轮 (fixed wheel ) 、同 心 方 向 轮 ( centered orientable
wheel) 和偏心方向轮 (off2centered orientable wheel) ,
当采用三个轮子 、γ为 0°时 ,见图 3. 轮子转动速
成全方位移动机器人.
度和车体速度之间的转换关系为
φ1
- sinα
co sα
l
x
φ2
= Jξ = -
1 r
- sin (α + 2/ 3π)

kinematics(动力学)1动力学课件

kinematics(动力学)1动力学课件

The subjects that occupied physical scientists through the end of the nineteenth century----mechanics, light, heat, sound, electricity and magnetism-------are usually referred to as classical physics.
Velocity is the rate at which the position changes. • Average Velocity The average velocity of a particle during the time interval Δt is defined as the ratio of the displacement to the time interval.
It is classical physics we must master to understand the macroscopic world we live in, and classical physics is the main subject of the first part of the course.
K Δr and Δr
K Δr ≠ Δr
#mech001
Which of the following statements is (are) true ? (a) Δr is the magnitude of the displacement .
G (b) Δr is the magnitude of the displacement.
z
P1
G v1

一级反应动力学、二级反应动力学基本原理

一级反应动力学、二级反应动力学基本原理
Wikipedia
Pseudo first order reactions
伪一级反应
pseudo-first order: concentration of one reactant remains essentially constant over time (often because it is in large excess compared to the other reactant)
kineticssayhowfastareactionhappenssequenceofstepsinthereactionandsomeofthefactorsthatcontroltheratesofreactions动力学则说明反应发生的速率有多快反应步骤的顺序以及控制反应速率的一些因素furtherreadingchapter3inhobbsrateofreactionistypicallymeasuredasthechangeinconcentrationmoleslwithtime反应速率通常通过浓度moll随时间的变化来测量thischangemaybeadecreaseoranincrease改变可能是增加的也可能是减小的likewisetheconcentrationchangemaybeofreactantsorproducts同样改变浓度的物质可能是反应物也可能是生成物反应速率浓度时间ratehasunitsofmolesperliterperunittimems1mh1速率的单位是摩尔每升每单位时间如ms1mh1considerthehypotheticalreaction对于这个假设的反应aabb?ccddwecanwritenotetheuseofthenegativesign注意负号的使用rateisdefinedasapositivequantity反应速率被定义为正量rateofdisappearanceofareactantisnegative那么反应物的消耗速率就是负的2n2o5g?4no2go2gratemaybeexpressedinthreemainways

物理第二站

物理第二站

ˆ ˆ ay ˆ a axi j az k
a ax ay az
2 2 2
ˆ j
ˆa a au
Magnitude
unit vector
ˆ i
2016-3-3
ˆa 1 or ua 1 u
phypzq@ 12
Chapter 2 Kinematics H-3 Adding Vectors
Chapter 2 Kinematics
These controls in the cockpit of a commercial aircraft assist the pilot in maintaining control over the velocity of the aircraft--how fast it is traveling and in what direction it is traveling—allowing it to land safely. Quantities that are defined by both a magnitude and a direction, such as velocity, are called vector quantities.
Work as a Dot Product

F
W FS
s
(constant force)
2016-3-3
phypzq@
22
Chapter 2 Kinematics *Cross product* (or vector product )of two vectors
ˆ ay ˆ a axi j
2016-3-3
o
φ
ax

Kinematic Control Robot Movement

Kinematic Control Robot Movement

Kinematic Control Robot MovementRobots are becoming increasingly prevalent in our society, and one area where they are making a significant impact is in the field of kinematic control for robot movement. Kinematic control refers to the use of mathematical equations to determine the motion of a robot's end effector, allowing for precise and accurate movement. This technology has a wide range of applications, from manufacturing and assembly to medical and surgical procedures. However, there are several challenges and considerations that must be addressed when implementing kinematic control for robot movement.One of the primary challenges in kinematic control is ensuring the accuracy and precision of the robot's movements. This is particularly important in applications such as surgery, where even the smallest deviation from the intended path can have serious consequences. To address this challenge, engineers and researchers are constantly developing and refining algorithms and control systems that can account for factors such as friction, backlash, and other sources of error. Additionally, advances in sensor technology, such as the use of force feedback and vision systems, are helping to improve the accuracy of kinematic control.Another consideration in kinematic control is the need to balance speed and accuracy. In many applications, such as manufacturing and assembly, it is important for robots to be able to move quickly while still maintaining precise control over their movements. Achieving this balance requires careful tuning of the robot's control systems and the use of advanced motion planning algorithms. This is an area of active research, as engineers seek to develop new techniques for optimizing the performance of kinematically controlled robots.In addition to technical challenges, there are also ethical and societal considerations that must be taken into account when implementing kinematic control for robot movement. For example, in the field of medicine, there is a growing concern about the potential for automation to replace human workers, particularly in surgical procedures. While kinematically controlled robots can offer significant benefits in terms of precision and repeatability, there is also a need to ensure that they are used in a way that complements and enhances the skills of human surgeons, rather than replacing them altogether.Furthermore, there are concerns about the potential for misuse of kinematically controlled robots, particularly in military applications. The ability to precisely control the movement of a robot, particularly in autonomous systems, raises questions about the ethical implications of using such technology in warfare. There is a need for careful consideration and regulation of the use of kinematic control in military robotics to ensure that it is used in a responsible and ethical manner.Despite these challenges and considerations, the potential benefits of kinematic control for robot movement are significant. In manufacturing and assembly, kinematically controlled robots can improve efficiency, quality, and safety. In medicine, they can enable new procedures and treatments that were previously not possible. In exploration and research, they can be used to access environments that are too dangerous for humans. As such, it is important to continue advancing the field of kinematic control while also addressing the associated challenges and considerations.In conclusion, kinematic control for robot movement is a rapidly advancing field with a wide range of applications and potential benefits. However, there are several challenges and considerations that must be addressed, from technical issues related to accuracy and speed to ethical and societal concerns about the impact of this technology. By carefully considering these factors and continuing to advance the state of the art in kinematic control, we can ensure that this technology is used in a responsible and beneficial manner.。

Kinematics Motion in One Dimension在一维运动运动

Kinematics Motion in One Dimension在一维运动运动
Steeper the slope, the higher the value
What can you tell me about acceleration on these graphs?
Big 5 Equations
Definition of average velocity: (vi + vf)/2
○
√
√
√
√
Timeless: vf2=vi2 +2a∆x
√
√
√
○
√
Position: ∆x=vit +1/2at2
√
√
○
√
√
Problem Solving Strategies
Identify givens
▪ Look for hidden givens
Identify unknown(s) Compare givens and unknowns to equations
▪ In the beginning: chart
Re-read problem if stuck
*always show your work (G.U.E.S.S.)
Sample Problem
What is Starlin Castro’s acceleration as he runs toward first base if he reaches the base with a speed of 6.5 m/s? The distance between the plates is 27.432 meters .
Technical difference between calculating speed and velocity:

Lecture 1

5
• Foundations of Dynamics
– Newton’s laws
• I. The existence of inertial reference frame • II. In an inertial frame, F=ma • III. Action and reaction forces are equal and act in opposite directions
ME Graduate Course: Dynamics
1
About the course and Grading
• Bilingual Course • English final exam (? or !) • Attendance is strongly recommended (for there is no Chinese textbooks) • In-class Practice (10%) • W/O a project (a 10% project by using MATLAB might be assigned depending on the schedule)
• Intrinsic coordinates
– Path Variables:
• The definition of the unit vectors and of the position relies on knowledge of the path
15
Path Variables
16
∆s →0
25
2
Reference Books
• Advanced Engineering Dynamics (2nd Edition, Jerry Ginsberg, Cambridge University Press 1995)

自闭症的知觉特异性与知觉功能促进化理论


N-back 工作记忆任务
左侧顶叶激活较强，与前额 右侧额叶和顶叶激活， 颞叶下
叶区域活动联系密切
方和枕叶后方有更多的激活
否
Müller 等人 [24]
枕 区 和 额 叶 皮 层 （BA8 和 10）的激活
否
Pierce 等人 [25]
面孔识别任务
顶下回、颞上沟、杏仁核激 杏仁核没有被激活， 显示独特
心理研究 Psychological Research 2012，5（4）：13-19
13
自闭症的知觉特异性与知觉功能促进化理论
吴 冉 徐光兴
（华东师范大学心理与认知科学学院，上海 200062）
摘 要：知觉特异性是自闭症的典型症状之一，掌握自闭症的特异性知觉特征对理解自闭症的认知、行为及其诊断、治疗有重要意 义。 21 世纪初提出的知觉功能促进化理论很好地解释了自闭症的知觉特异性特征，引起了科学研究与临床领域的重视。 本文介绍 了自闭症的知觉功能促进化理论及其发展，并以该理论为框架，介绍自闭症的知觉特异性特征及其对自闭症行为特征的影响，期 望通过对知觉特异性特征的理解和理论反思，能够对自闭症的教育与治疗有所裨益。 关键词：自闭症；知觉特异性；知觉功能促进化
1 引言
自闭症被定义为一种特殊类型的广泛性发展 障 碍 ，自 从 Kanner 和 Asperger 几 乎 同 时 首 次 对 自 闭症进行了描述后［1－2］，自闭症复杂的病 因 、症 状 就 吸引了很多研究者的目光。 特异性的知觉功能是 自闭症典型的特征之一。 越来越多研究证据表明， 知觉特异性在自闭症的行为和认知表型中具有突 出作用。
通讯作者：徐光兴，男，教授，博士生导师。 Email: gxxu@
14
心理

0101Chapter 1 Kinematics of a Particle

a dv x i v y j v z k axi a y j azk v dt
(1.3)
where the rectangular components see Fig. 1. l (b). Sample problem 1.1 In Fig. the crank OA of the scotch yoke is turning with a constant angular velocity ω rad/s. Derive the expressions for the displacement, velocity, and acceleration of the sliding member.
y 8mm / s 2 ay v
Substituting t=2.090s, we obtain
机械程系
3
机械基础
Vector Mechanics
Statics and Dynamics
a x 37.8mm / s 2
and
a y 8mm / s 2
Therefore the acceleration vector at y=30mm a=37.8i +8j mm/ s 2 The pictorial representation of a is
R sin2ωt 2
z=Rsin 2 ωt
where R and ω are constants. (1) By calculating the magnitude of the position vector r show that the path line on a sphere of radius R, centered at the origin of the coordinate system. (2) Determine the rectangular and the magnitudes of the velocity and acceleration vectors. Solution Part 1 The magnitude of the position vector can be calculated using r 2 x 2 y 2 z 2 . Substituting the given Expressions for the rectangular coordinates we obtain

机械系统动力学英语版介绍


Rewriting:
x(t) a1(cosnt j sinnt) +a2 (cosnt j sinnt)
(a1 a2 ) cosnt j(a1 - a2 ) sin nt
Giving:
x(t) A1 cosnt A2 sinnt
Rearrange to yield the familiar equation of motion:
➢Physical model
➢Mathematical model
Restoring force
Spring
Damping element
Damping force
Undamped Free Vibration
vibration ➢ Apply numerical tools to obtain the time response
of SDOF system
Single degree of freedom systems
• When one variable can describe the motion of a structure or a system of bodies, then we may call the system a 1-D system or a single degree of freedom (SDOF) system.
3. To understand concepts of modal analysis. 4. To understand concepts in passive and active vibration
control systems.
Prerequisites: The most important prerequisite is ordinary differential equations. You should be prepared to review undergraduate differential equations if necessary.
  1. 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
  2. 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
  3. 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

Table 1: D-H parameters of the single caster wheel Joint i αi ai θi di 1 −π/2 0 σ 0 2 π/2 0 0 rρ 3 0 0 φ 0 The position of the end-effector with respect to Frame O is: rρcσ + hcσ+φ 0 pE = rρsσ + hsσ+φ 0
(1)
where r is the wheel radius, cσ = Cos(σ ) and cσ+φ = Cos(σ + φ). The same applies to the sines. The end-effector is located at the center of the mobile base, therefore the length of the second link of the model above is taken as h, where h is the radius of the mobile base. When differentiated, the position vector x will provide the velocity vector of the end-effector, or upon rearranging, the Jacobian matrix and the joint velocity vector. Note that when differentiating rρ with respect to σ and φ, it is taken as the constant value of the offset b, which is the real physical distance. However, when differentiating it respect to ρ, it is taken as a variable with respect to time, rρ) = rρ ˙. resulting in δ(δt Adding the rotational components (the rotational axes of σ and φ) into the Jacobian matrix, we obtain: −hsσ+φ − rρsσ rcσ −hsσ+φ 0 (2) J = hcσ+φ + rρcσ rsσ hcσ+φ 1 0 1 where x ˙ ˙ = J ˙ = y x ˙ θ σ ˙ ρ ˙ ˙ φ
KINEMATICS AND DYNAMICS OF AN OMNIDIRECTIONAL MOBILE PLATFORM WITH POWERED CASTER WHEELS Maung ThanZaw† Denny Oetomo† Marcelo H. Ang Jr. Ng Teck Khim National University of Singapore † Singapore Institute of Manufacturing Technology
2
Kinematics Modelling of a Single Caster Wheel
In the formulation of kinematics model, we treat the wheel module as a serial link manipulator with two revolute joints and one prismatic joint in instantaneous time. The point of wheel contact with the floor is taken as a revolute joint (σ ). This is a passive joint with no position feedback, as this is the twist angle between the wheel contact and the floor. With the assumption of no slippage, the forward rolling motion of the wheel is treated as a prismatic joint (rρ) where r is the wheel radius and ρ is the angular displacement is radians. The steering joint is the last revolute joint (φ) of the system. See Figure 1. By instantaneous, we mean that the prismatic joint (rρ) provides an instantaneous linear translation that pushes the end-effector forward with respect to the floor. At the same time, the mechanism has a set length of b (the wheel offset) between the rotation axes of σ and φ. The D-H parameter for the single caster wheel modelled as a serial manipulator is shown in Table 1. The Frame O is an instantaneous frame that is always parallel to the world (absolute) frame, but moves together with the wheel. In other words, it is attached to the contact point between the wheel and the floor.
T.Z. Maung, D. Oetomo, M.H. Ang Jr., T.K. Ng, “Kinematics and Dynamics of an Omnidirectional Mobile Platform with Powered Caster Wheels,” International Symposium on Dynamics and Control, Hanoi, Vietnam, 15-20 September, 2003.
1
Introduction
Omnidirectional wheeled mobile robots have been an active research area over the past three decades. The advantages over the legged mobile robots are the ease of manufacture, high pay load, high efficiency, and the ability to perform tasks in congested and narrow environment. There are three types of wheels [1]: the conventional wheels, the omnidirectional wheels, and the ball wheel. The conventional wheels are the wheels that we see everyday, such as those on the cars and trolleys. An omnidirectional wheel is a disk-like wheel with a multitude of conventional wheels mounted on its periphery. The ball wheel is one that’s shaped like a ball. The ball wheel [2, 3] is difficult to implement as it is not possible to place an axel through the ball without sacrificing the usable workspace. It is difficult to transmit power to drive the wheel. There is also the practical need of keeping it robust from collected dust and dirt from the floor. There has been a lot of effort in the development of omnidirectional wheels [4, 5, 6]. Due to multiple number of small rollers on the periphery of the wheel, an undesirable vibration often exists in the motion. The conventional wheel is probably the simplest and most robust among the designs. However, not all conventional wheels are capable of providing omnidirec-
Abstract Mobile robots with omni-directional motion capabilities are very useful especially in mobile manipulation tasks and tasks in human environment. In this paper, we present the kinematics and dynamics of one class of omni-directional mobile robots that is driven by a 2 axis powered caster wheels with non-intersecting axes of motions (caster wheels with offset). Our derivation approach treats the each caster wheel as a serial manipulator and the entire system as a parallel manipulator generated by several serial manipulator with a cg the operational space formulation by Khatib