Inverse velocity analysis for line guidance five-axis robots

In this paper, inverse velocity problem for five-axis robots is investigated. The conventional method for a five-axis robot is to pseudo-inverse the 6×5 Jacobian matrix. The solution, primarily based on six freedoms inverse velocity analysis, is just an approximation with a least-square error. A five-axis robot can exactly guide an axis-symmetrical tool in 3-D space. Two exact solutions are provided for five-axis robots. One is based on the screw motion of the tool. The other is based on spherical angles of the tool to derive a 5×5 Jacobian matrix. A new type of singular configuration is discovered and is called the task singularity. The moving path of the line shaped tool is constructed as a ruled surface. Analysis of the angular acceleration shows the surface constructed based on the spherical angle representation has better characteristic. It is concluded that for five-axis robots, the tool position is better represented by five parameters rather than six parameters in order to get better solutions for inverse velocity as well as the motion planning.