Stiffness synthesis of 3-DOF planar 3RPR parallel mechanisms

Abstract

SUMMARYForce control is important in robotics research for safe operation in the interaction between a manipulator and a human operator. The elasticity center is a very important characteristic for controlling the force of a manipulator, because a force acting at the elasticity center results in a pure displacement of the end-effector in the same direction as the force. Similarly, a torque acting at the elasticity center results in a pure rotation of the end-effector in the same direction as the torque. A stiffness synthesis strategy is proposed for a desired elasticity center for three-degree-of-freedom (DOF) planar parallel mechanisms (PPM) consisting of three revolute-prismatic-revolute (3RPR) links. Based on stiffness analysis, the elasticity center is derived to have a diagonal stiffness matrix in an arbitrary configuration. The stiffness synthesis is defined to determine the configuration when the elasticity center and the diagonal matrix are given. The seven nonlinear system equations are solved based on one reference input. The existence and the solvability of the nonlinear system equations were analyzed using reduced Gröbner bases. A numerical example is presented to validate the method.

Grasp compliance achieved with a planar hand composed of multiple 3-joint fingers

“…In refs. [8,9], methods of stiffness synthesis using planar parallel mechanisms with specific constructions were developed. In refs.…”

Stiffness analysis of a 3-DOF parallel mechanism for engineering special machining

“…Stiffness design refers to optimization based on a certain stiffness analysis model with structural parameters as variables to improve the stiffness performance of the mechanism. A stiffness synthesis strategy was proposed for the desired elastic center of a 3-DOF parallel mechanism composed of 3RPR links (Wen et al, 2015). The Exechon parallel mechanism with over-constrained kinematic chain has attracted extensive attention in the research community and its stiff-H. Zhang et al: Stiffness analysis of a 3-DOF parallel mechanism ness has been studied by Zhang et al (2016).…”

“…Wen et al (2015),Zhang et al (2016),Li et al (2017),,Wang et al (2017) Stiffness modeling and analysis methods Enhance the anti-deformation ability of the mechanism and improve the movement accuracy and stability Sun et al (2016),Wu et al (2013),. Gosselin and Schreiber (2018),Fang et al (2020) Stiffness analysis of a 3-DOF parallel mechanism for engineering special machining Facing the requirements of complex surface machining tasks, a parallel mechanism with good stiffness performance is proposed.…”

A new synthesis method for planar Rubik’s cube mechanism

“…St-Onge et al 35 presented a new design of a deployable planar mechanisms with large expansion ratios, whose performances were expected to be better for larger scale mechanisms. Wen et al 36 investigated a stiffness synthesis strategy for 3RPR robots with desired stiffness at the elastic center. Nafees et al 37 carried out the synthesis of five-bar mechanism for two tracing points that generates the trajectory and transmits motion between two extreme positions.…”