On the Robot Singularity: A Novel Geometric Approach

[摘要] This paper addresses a novel geometric analysis method of the singularity and kinestatic characteristics of robots. For non-redundant robots, there exist two uniquely determined Jacobians – the screw-based Jacobian and the reciprocal Jacobian. Here, it is shown that if some of the reciprocal products between the column screws of the two Jacobians are close to zero, the robot is in the vicinity of a singular configuration and the corresponding columns of the Jacobian are involved in the singularity. From this observation, an invariant measure of closeness to a singularity is presented using the reciprocal products. Furthermore, by considering the reciprocal products between the actuated joint screws and column screws of the Jacobian, this measure is extended so that the concept of the kinestatic characterization index is presented for parallel robots. Since it is defined as the ratio of reciprocal products from the uniqueness of the two Jacobians, it represents a unique invariant characteristic of robots. ...

[学科分类] 自动化工程

[关键词] Invariant measure of singularity;kinestatic characterization index;singularity of the robot;parallel manipulator;theory of screws