Abstract
The inverse kinematics is a fundamental robotics. In order to control the position and orientation of the end-effector of a robot, the inverse kinematics solution is necessary. In this paper, work-space is used as the set of reachable positions and orientation of the robot's end-effector, and joint-space is used as the set of reachable configurations of the robot's joint limits. The position and the orientation of a robot's end-effector is defined by a set of the robot's joints angles, that is to say the position and orientation of a robot's end-effect is defined by the mapping from joint-space to work-space. A robot is assured to be non-redundant and the new method is proposed to classify the inverse kinematics solution, by resolving the Jacobian of robot. So the dimension of work-space is equal to the dimension of joint-space. First the method of manifold is used to make the character of joint-space clear. And then, the method of mapping is used to define shape-space that is the base-space in joint-space. And then, the method of mapping is used to make clear the number of inverse kinematics solution. In the last the method above is used to analyse the 2-joint (RR) SCARA type robot and the 3-joint (RRR) PUMA type robot.
