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 orientationsingularity path planning are explored, respectively. For the position-singularity path planning, after obtaining the positionsingularity 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.

Self-excited vibration of a 3-PRR planar parallel robot

“…13,14 Due to mutual restraints among the various requirements, it is generally difficult to obtain a completely singularity-free workspace by optimum design method. In this case, the methods of trajectory optimization 15,16 or working mode conversion 17 can be utilized to avoid the singularity and realize the singularity-free motion inside the workspace. The redundantly actuated mechanisms have some good properties 18 and it is also an effective technique to introduce redundancies to realize the purpose of singularity avoidance.…”

“…As mentioned above, the research on singularity mainly focuses on theoretical analysis, such as singularity classification 6–10 and singularity avoidance. 13–20 However, few studies have investigated the dynamic characteristics of parallel robots at singularities. Moreover, the research on self-excited vibration of parallel robot is also very rare.…”

Screw theory based method to formulate local Jacobian’ magnitude estimator contours for 6 DoF robots

“…The literature has focused on the avoidance of singularities, 9,15–24 which is the primary requirement in any robotic manipulation. Different control architectures and path planning methods have been proposed.…”

High-order singularities of 5R planar parallel robots

“…26 Near a singularity of this type, the robot becomes, in general, uncontrollable due to the unboundedly growing inverse dynamic solution. 27,28 Several researchers have studied singularity-free path planning 29,30 and singularity-free zones within the workspace 31−36 of parallel manipulators. However, parallel singularities are usually encountered inside the workspace, 25 and therefore the usable regions of the workspace of parallel robots are mainly small.…”