A robust geometric method of singularity avoidance for kinematically redundant planar parallel robot manipulators

Abstract

Jacobian-based methods of singularity analysis are known to be unreliable when applied to kinematically redundant parallel robot manipulators, due to their potential to miss certain singularities and incorrectly identify others in the manipulator's workspace. In this paper, a geometric method of singularity avoidance for kinematically redundant planar parallel robot manipulators is presented, which firstly determines the manipulator's proximity to a singularity and then computes how the kinematically redundant degree(s) of freedom should be optimised for the given pose of the end-effector. The singularity analysis is conducted by examining the mechanism in terms of the instantaneous centres of rotation of its corresponding mobility one sub-mechanisms when all but one of the actuators are locked, where the manipulator is in a type-II singularity when these points either are indeterminable or coincide with one another, and an index, r min , is introduced which describes the minimum normalised distance from such conditions being met. A predictor-corrector method is employed to compute the configuration for which r min is optimised, and is reachable without crossing a singularity. Finally, the advantages of the geometric method of singularity analysis are shown in comparison to traditional Jacobian-based methods when applied to kinematically redundant parallel robot manipulators.

Kinematics Analysis and Singularity Avoidance of a Parallel Mechanism with Kinematic Redundancy

“…In the same way, the expressions for actuating lengths L 2 and L 3 can be obtained by the closed-loop equations of limb 2 and limb 3, as shown in Eqs. (30) and (31). (23)…”

“…By analyzing the Jacobian matrix and singular image of the mechanism, the singular position of the mechanism can be obtained [31][32][33]. When θ i1 = π/2 and θ i2 = 0°of a limb, the mechanism will have a singular position 1, as shown in Figure 20a.…”

Kinematics Analysis and Singularity Avoidance of a Parallel Mechanism with kinematic redundancy

“…( 41)-(42). By analyzing the Jacobian matrix and singular image of the mechanism, the singular position of the mechanism can be obtained [31,32,33]. When θi1 =π/2 and θi2=0°of a limb, the mechanism will have a singular position①; When θi1 =θi2=π/2 of the three limbs, the mechanism will have a singular position②; When θi1 =0° of a limb, the mechanism produces a singular position③.…”

Kinematic of 4SPRR-SPR parallel robots based on VQTAM

“…It's assumed that the relationship between local input and output can be expressed linearly, so the LLR can be performed as shown in equation (19).…”

“…16,17 For instance, M. Garcia-Murillo et al 18 proposed a 2(3-RRPS) parallel robot and analyzed its workspace. Nicholas Baron, et al 19 displayed a family of kinematically redundant planar parallel robots, and presented a geometric method of singularity avoidance. In addition, the cable-driven manipulators are a class of PMs, where the end-effector is displaced by means of servo-actuated extendable cables.…”