机器人学基础_第3章_机器人运动学.ppt

中南大学 蔡自兴，谢 斌 zxcai, xiebin@mail.csu.edu.cn 2010 3.0 Introduction to Robot Kinematics Kinematics treats motion without regard to the forces that cause it. Within the science of kinematics one studies the position, velocity, acceleration, and all higher order derivatives of the position variables (with respect to time or any other variable). 3.0 Introduction to Robot Kinematics In manipulator robotics, there are two kinematics tasks: Direct (also forward) kinematics – Given are joint relations (rotations, translations) for the robot arm. Task: What is the orientation and position of the end effector? Inverse kinematics – Given is desired end effector position and orientation. Task: What are the joint rotations and orientations to achieve this? Example of Direct Kinematics Define position of end effector and the joint variable， According to geometry： Example of Inverse Kinematics Example of Inverse Kinematics Mechanics of a manipulator can be represented as a kinematics chain of rigid bodies (links) connected by revolute or prismatic joints. One end of the chain is constrained to a base, while an end effector is mounted to the other end of the chain. The resulting motion is obtained by composition of the elementary motions of each link with respect to the previous one. 3.1.3 T-Matrix and A-Matrix Denavit-Hartenberg Parameters 4 D-H parameters 3 fixed link parameters 1 joint variable αi and ai : describe the Link i di and θi : describe the Link’s connection 3.1.3 T-Matrix and A-Matrix 3.1.3 T-Matrix and A-Matrix 3.1.3 T-Matrix and A-Matrix 3.1.3 T-Matrix and A-Matrix 3.1.3 T-Matrix and A-Matrix 3.1.3 T-Matrix and A-Matrix 3.1.3 T-Matrix and A-Matrix 这种关系可由表示连杆相对位置的四个齐次变换来描述，并叫做 矩阵。此关系式为： (3.12) 展开上式可得 ： （3.13） 3.2 Solving Kinematics Eq