Singularity property and singularity-free path planning of the Gough–Stewart parallel mechanism

Abstract

Singularity affects the performance of the parallel mechanisms seriously and so should be avoided as the mechanisms work. It is necessary to obtain the distribution of the singularity locus in the task space of a parallel mechanism and then further explore singularity avoidance. This article mainly deals with the singularity-free path planning of the widely used Gough–Stewart parallel mechanism. After obtaining the characteristics of the position-singularity locus for a constant orientation and the orientation-singularity locus for a given position, the position-singularity path planning and orientation-singularity path planning are explored, respectively. For the position-singularity path planning, after obtaining the position-singularity locus equation and analyzing the geometric property of the position-singularity curve in a moving plane, a general method for identifying the probability of existence of a singularity-free path connecting two given points in the moving plane is illustrated, and then the technique of the singularity-free path planning is also represented in case if a singularity-free path exists. For the orientation-singularity path planning, the orientation kinematic equation and the time optimal orientation path of a rigid body are constructed using the quaternion algebra theory, respectively. After analyzing the orientation-singularity locus and using the results of time optimal orientation path of a rigid body, the method of time optimal orientation path planning of the mechanism is investigated. The validation of the aforementioned methods of two types of singularity-free path is tested and verified by applying numerical examples. The research has important theoretical significance and practical reference value for the exploration of the singularity avoidance of the parallel mechanism.