RobotArmKinematics=DHintroppt:機器人手臂的運動學=DH.ppt

上傳人:za****8 文檔編號:15178114 上傳時間:2020-08-05 格式:PPT 頁數(shù):75 大?。?.47MB
收藏 版權(quán)申訴 舉報 下載
RobotArmKinematics=DHintroppt:機器人手臂的運動學=DH.ppt_第1頁
第1頁 / 共75頁
RobotArmKinematics=DHintroppt:機器人手臂的運動學=DH.ppt_第2頁
第2頁 / 共75頁
RobotArmKinematics=DHintroppt:機器人手臂的運動學=DH.ppt_第3頁
第3頁 / 共75頁

下載文檔到電腦,查找使用更方便

14.9 積分

下載資源

還剩頁未讀,繼續(xù)閱讀

資源描述:

《RobotArmKinematics=DHintroppt:機器人手臂的運動學=DH.ppt》由會員分享,可在線閱讀,更多相關(guān)《RobotArmKinematics=DHintroppt:機器人手臂的運動學=DH.ppt(75頁珍藏版)》請在裝配圖網(wǎng)上搜索。

1、More details and examples on robot arms and kinematics,Denavit-Hartenberg Notation,INTRODUCTION,Forward Kinematics: to determine where the robots hand is? (If all joint variables are known) Inverse Kinematics: to calculate what each joint variable is? (If we desire that the hand be located at a part

2、icular point),Direct Kinematics,Direct Kinematics with no matrices,Where is my hand?,Direct Kinematics: HERE!,Direct Kinematics,Position of tip in (x,y) coordinates,Direct Kinematics Algorithm,1) Draw sketch 2) Number links. Base=0, Last link = n 3) Identify and number robot joints 4) Draw axis Zi f

3、or joint i 5) Determine joint length ai-1 between Zi-1 and Zi 6) Draw axis Xi-1 7) Determine joint twist i-1 measured around Xi-1 8) Determine the joint offset di 9) Determine joint angle i around Zi 10+11) Write link transformation and concatenate,Often sufficient for 2D,Kinematic Problems for Mani

4、pulation,Reliably position the tip - go from one position to another position Dont hit anything, avoid obstacles Make smooth motions at reasonable speeds and at reasonable accelerations Adjust to changing conditions - i.e. when something is picked up respond to the change in weight,ROBOTS AS MECHANI

5、SMs,Robot Kinematics: ROBOTS AS MECHANISM,Fig. 2.1 A one-degree-of-freedom closed-loop four-bar mechanism,Multiple type robot have multiple DOF. (3 Dimensional, open loop, chain mechanisms),Fig. 2.2 (a) Closed-loop versus (b) open-loop mechanism,Chapter 2Robot Kinematics: Position Analysis,Fig. 2.3

6、Representation of a point in space,A point P in space : 3 coordinates relative to a reference frame,Representation of a Point in Space,Chapter 2Robot Kinematics: Position Analysis,Fig. 2.4 Representation of a vector in space,A Vector P in space : 3 coordinates of its tail and of its head,Representat

7、ion of a Vector in Space,Chapter 2Robot Kinematics: Position Analysis,Fig. 2.5 Representation of a frame at the origin of the reference frame,Each Unit Vector is mutually perpendicular. : normal, orientation, approach vector,Representation of a Frame at the Origin of a Fixed-Reference Frame,Chapter

8、2Robot Kinematics: Position Analysis,Fig. 2.6 Representation of a frame in a frame,Each Unit Vector is mutually perpendicular. : normal, orientation, approach vector,Representation of a Frame in a Fixed Reference Frame,The same as last slide,Chapter 2Robot Kinematics: Position Analysis,Fig. 2.8 Repr

9、esentation of an object in space,An object can be represented in space by attaching a frame to it and representing the frame in space.,Representation of a Rigid Body,Chapter 2Robot Kinematics: Position Analysis,A transformation matrices must be in square form. It is much easier to calculate the inve

10、rse of square matrices. To multiply two matrices, their dimensions must match.,HOMOGENEOUS TRANSFORMATION MATRICES,Representation of Transformations of rigid objects in 3D space,Chapter 2Robot Kinematics: Position Analysis,Fig. 2.9 Representation of an pure translation in space,A transformation is d

11、efined as making a movement in space. A pure translation. A pure rotation about an axis. A combination of translation or rotations.,Representation of a Pure Translation,identity,Same value a,Chapter 2Robot Kinematics: Position Analysis,Fig. 2.10 Coordinates of a point in a rotating frame before and

12、after rotation around axis x.,Assumption : The frame is at the origin of the reference frame and parallel to it.,Fig. 2.11 Coordinates of a point relative to the reference frame and rotating frame as viewed from the x-axis.,Representation of a Pure Rotation about an Axis,Projections as seen from x a

13、xis,x,y,z n, o, a,Fig. 2.13 Effects of three successive transformations,A number of successive translations and rotations.,Representation of Combined Transformations,Order is important,x,y,z n, o, a,ni,oi,ai,T1,T2,T3,Fig. 2.14 Changing the order of transformations will change the final result,Order

14、of Transformations is important,x,y,z n, o, a,translation,Chapter 2Robot Kinematics: Position Analysis,Fig. 2.15 Transformations relative to the current frames.,Example 2.8,Transformations Relative to the Rotating Frame,translation,rotation,MATRICES FORFORWARD AND INVERSE KINEMATICS OF ROBOTS,For po

15、sition For orientation,Chapter 2Robot Kinematics: Position Analysis,Fig. 2.17 The hand frame of the robot relative to the reference frame.,Forward Kinematics Analysis: Calculating the position and orientation of the hand of the robot. If all robot joint variables are known, one can calculate where t

16、he robot is at any instant. .,FORWARD AND INVERSE KINEMATICS OF ROBOTS,Chapter 2Robot Kinematics: Position Analysis,Forward Kinematics and Inverse Kinematics equation for position analysis : (a) Cartesian (gantry, rectangular) coordinates. (b) Cylindrical coordinates. (c) Spherical coordinates. (d)

17、Articulated (anthropomorphic, or all-revolute) coordinates.,Forward and Inverse Kinematics Equations for Position,Chapter 2Robot Kinematics: Position Analysis,IBM 7565 robot All actuator is linear. A gantry robot is a Cartesian robot.,Fig. 2.18 Cartesian Coordinates.,Forward and Inverse Kinematics E

18、quations for Position (a) Cartesian (Gantry, Rectangular) Coordinates,Chapter 2Robot Kinematics: Position Analysis,2 Linear translations and 1 rotation translation of r along the x-axis rotation of about the z-axis translation of l along the z-axis,Fig. 2.19 Cylindrical Coordinates.,Forward and Inve

19、rse Kinematics Equations for Position: Cylindrical Coordinates,cosine,sine,Chapter 2Robot Kinematics: Position Analysis,2 Linear translations and 1 rotation translation of r along the z-axis rotation of about the y-axis rotation of along the z-axis,Fig. 2.20 Spherical Coordinates.,Forward and Invers

20、e Kinematics Equations for Position (c) Spherical Coordinates,Chapter 2Robot Kinematics: Position Analysis,3 rotations - Denavit-Hartenberg representation,Fig. 2.21 Articulated Coordinates.,Forward and Inverse Kinematics Equations for Position (d) Articulated Coordinates,Chapter 2Robot Kinematics: P

21、osition Analysis, Roll, Pitch, Yaw (RPY) angles Euler angles Articulated joints,Forward and Inverse Kinematics Equations for Orientation,Chapter 2Robot Kinematics: Position Analysis,Roll: Rotation of about -axis (z-axis of the moving frame) Pitch: Rotation of about -axis (y-axis of the moving frame)

22、 Yaw: Rotation of about -axis (x-axis of the moving frame),Fig. 2.22 RPY rotations about the current axes.,Forward and Inverse Kinematics Equations for Orientation (a) Roll, Pitch, Yaw(RPY) Angles,Chapter 2Robot Kinematics: Position Analysis,Fig. 2.24 Euler rotations about the current axes.,Rotation

23、 of about -axis (z-axis of the moving frame) followed by Rotation of about -axis (y-axis of the moving frame) followed by Rotation of about -axis (z-axis of the moving frame).,Forward and Inverse Kinematics Equations for Orientation (b) Euler Angles,Chapter 2Robot Kinematics: Position Analysis,Assum

24、ption : Robot is made of a Cartesian and an RPY set of joints.,Assumption : Robot is made of a Spherical Coordinate and an Euler angle.,Another Combination can be possible,Denavit-Hartenberg Representation,Forward and Inverse Kinematics Equations for Orientation,Roll, Pitch, Yaw(RPY) Angles,Forward

25、and Inverse Transformations for robot arms,Fig. 2.16 The Universe, robot, hand, part, and end effecter frames.,Steps of calculation of an Inverse matrix: Calculate the determinant of the matrix. Transpose the matrix. Replace each element of the transposed matrix by its own minor (adjoint matrix). Di

26、vide the converted matrix by the determinant.,INVERSE OF TRANSFORMATION MATRICES,Identity Transformations,We often need to calculate INVERSE MATRICES It is good to reduce the number of such operations We need to do these calculations fast,How to find an Inverse Matrix B of matrix A?,Inverse Homogene

27、ous Transformation,Homogeneous Coordinates,Homogeneous coordinates: embed 3D vectors into 4D by adding a “1” More generally, the transformation matrix T has the form:,a11 a12 a13 b1 a21 a22 a23 b2 a31 a32 a33 b3 c1 c2 c3 sf,It is presented in more detail on the WWW!,For various types of robots we ha

28、ve different maneuvering spaces,For various types of robots we calculate different forward and inverse transformations,For various types of robots we solve different forward and inverse kinematic problems,Forward and Inverse Kinematics: Single Link Example,Forward and Inverse Kinematics: Single Link

29、 Example,easy,Denavit Hartenberg idea,Denavit-Hartenberg Representation :,Fig. 2.25 A D-H representation of a general-purpose joint-link combination, Simple way of modeling robot links and joints for any robot configuration, regardless of its sequence or complexity., Transformations in any coordinat

30、es is possible., Any possible combinations of joints and links and all-revolute articulated robots can be represented.,DENAVIT-HARTENBERG REPRESENTATION OF FORWARD KINEMATIC EQUATIONS OF ROBOT,Chapter 2Robot Kinematics: Position Analysis, : A rotation angle between two links, about the z-axis (revol

31、ute). d : The distance (offset) on the z-axis, between links (prismatic). a : The length of each common normal (Joint offset). : The “twist” angle between two successive z-axes (Joint twist) (revolute) Only and d are joint variables.,DENAVIT-HARTENBERG REPRESENTATION Symbol Terminologies :,Links are

32、 in 3D, any shape, associated with Zi always,Only rotation,Only translation,Only offset,Only offset,Only rotation,Axis alignment,DENAVIT-HARTENBERG REPRESENTATION for each link,4 link parameters,Chapter 2Robot Kinematics: Position Analysis, : A rotation angle between two links, about the z-axis (rev

33、olute). d : The distance (offset) on the z-axis, between links (prismatic). a : The length of each common normal (Joint offset). : The “twist” angle between two successive z-axes (Joint twist) (revolute) Only and d are joint variables.,DENAVIT-HARTENBERG REPRESENTATION Symbol Terminologies :,Example

34、 with three Revolute Joints,Denavit-Hartenberg Link Parameter Table,The DH Parameter Table,Apply first,Apply last,Denavit-Hartenberg Representation of Joint-Link-Joint Transformation,Notation for Denavit-Hartenberg Representation of Joint-Link-Joint Transformation,Alpha applied first,Four Transforma

35、tions from one Joint to the Next,Order of multiplication of matrices is inverse of order of applying them Here we show order of matrices,Joint-Link-Joint,Denavit-Hartenberg Representation of Joint-Link-Joint Transformation,Alpha is applied first,How to create a single matrix A n,EXAMPLE: Denavit-Har

36、tenberg Representation of Joint-Link-Joint Transformation for Type 1 Link,Final matrix from previous slide,substitute,substitute,Numeric or symbolic matrices,The Denavit-Hartenberg Matrix for another link type,Similarity to Homegeneous: Just like the Homogeneous Matrix, the Denavit-Hartenberg Matrix

37、 is a transformation matrix from one coordinate frame to the next. Using a series of D-H Matrix multiplications and the D-H Parameter table, the final result is a transformation matrix from some frame to your initial frame.,Put the transformation here for every link,In DENAVIT-HARTENBERG REPRESENTAT

38、ION we must be able to find parameters for each link So we must know link types,Links between revolute joints,ln=0,Type 3 Link,Joint n+1,Joint n,dn=0,Link n,xn-1,xn,ln=0 dn=0,Type 4 Link,Origins coincide,n-1,Joint n+1,Joint n,Part of dn-1,Link n,xn-1,yn-1,xn,n,Links between prismatic joints,Forward

39、and Inverse Transformations on Matrices,Start point: Assign joint number n to the first shown joint. Assign a local reference frame for each and every joint before or after these joints. Y-axis is not used in D-H representation.,DENAVIT-HARTENBERG REPRESENTATION PROCEDURES, All joints are represente

40、d by a z-axis. (right-hand rule for rotational joint, linear movement for prismatic joint) The common normal is one line mutually perpendicular to any two skew lines. Parallel z-axes joints make a infinite number of common normal. Intersecting z-axes of two successive joints make no common normal be

41、tween them(Length is 0.).,DENAVIT-HARTENBERG REPRESENTATION Procedures for assigning a local reference frame to each joint:,Chapter 2Robot Kinematics: Position Analysis, : A rotation about the z-axis. d : The distance on the z-axis. a : The length of each common normal (Joint offset). : The angle be

42、tween two successive z-axes (Joint twist) Only and d are joint variables.,DENAVIT-HARTENBERG REPRESENTATION Symbol Terminologies Reminder:,Chapter 2Robot Kinematics: Position Analysis,(I) Rotate about the zn-axis an able of n+1. (Coplanar) (II) Translate along zn-axis a distance of dn+1 to make xn a

43、nd xn+1 colinear. (III) Translate along the xn-axis a distance of an+1 to bring the origins of xn+1 together. (IV) Rotate zn-axis about xn+1 axis an angle of n+1 to align zn-axis with zn+1-axis.,DENAVIT-HARTENBERG REPRESENTATION The necessary motions to transform from one reference frame to the next.,

展開閱讀全文
溫馨提示:
1: 本站所有資源如無特殊說明,都需要本地電腦安裝OFFICE2007和PDF閱讀器。圖紙軟件為CAD,CAXA,PROE,UG,SolidWorks等.壓縮文件請下載最新的WinRAR軟件解壓。
2: 本站的文檔不包含任何第三方提供的附件圖紙等,如果需要附件,請聯(lián)系上傳者。文件的所有權(quán)益歸上傳用戶所有。
3.本站RAR壓縮包中若帶圖紙,網(wǎng)頁內(nèi)容里面會有圖紙預覽,若沒有圖紙預覽就沒有圖紙。
4. 未經(jīng)權(quán)益所有人同意不得將文件中的內(nèi)容挪作商業(yè)或盈利用途。
5. 裝配圖網(wǎng)僅提供信息存儲空間,僅對用戶上傳內(nèi)容的表現(xiàn)方式做保護處理,對用戶上傳分享的文檔內(nèi)容本身不做任何修改或編輯,并不能對任何下載內(nèi)容負責。
6. 下載文件中如有侵權(quán)或不適當內(nèi)容,請與我們聯(lián)系,我們立即糾正。
7. 本站不保證下載資源的準確性、安全性和完整性, 同時也不承擔用戶因使用這些下載資源對自己和他人造成任何形式的傷害或損失。

相關(guān)資源

更多
正為您匹配相似的精品文檔
關(guān)于我們 - 網(wǎng)站聲明 - 網(wǎng)站地圖 - 資源地圖 - 友情鏈接 - 網(wǎng)站客服 - 聯(lián)系我們

copyright@ 2023-2025  zhuangpeitu.com 裝配圖網(wǎng)版權(quán)所有   聯(lián)系電話:18123376007

備案號:ICP2024067431-1 川公網(wǎng)安備51140202000466號


本站為文檔C2C交易模式,即用戶上傳的文檔直接被用戶下載,本站只是中間服務平臺,本站所有文檔下載所得的收益歸上傳人(含作者)所有。裝配圖網(wǎng)僅提供信息存儲空間,僅對用戶上傳內(nèi)容的表現(xiàn)方式做保護處理,對上載內(nèi)容本身不做任何修改或編輯。若文檔所含內(nèi)容侵犯了您的版權(quán)或隱私,請立即通知裝配圖網(wǎng),我們立即給予刪除!