Abstract
In order to design and control a robotic arm on the scientific basis, it is necessary to evaluate its manipulation performance. In this paper, the use of the Jacobian as the performance index is discussed from the kinematic and static standpoint of view.
The value of the Jacobian is related to the homogeneity of the transformation from the joint coordinates to the workspace coordinates and, therefore, can be an index for the manipulation skill at a point in the workspace. The index takes the minimum value at singular points at which the arm loses capability of moving in a certain direction and is least dexterous.
Color graphics display of the distribution of the index value gives an overall understanding of the manipulation performance. This is illustrated by numerical examples for two different types of robotic arms with six revolute joints.
As examples of the application of the index, trajectory planning and optimal design of arm mechanisms are described. With the index, it is possible to plan trajectories scientifically. Numerical results for avoiding singular points and turning a crank with the best hand orientation are presented. The average of the index value over the whole workspace can be an index for the comparison of different arm mechanisms. A two link arm is designed using the index.
