Stiffness Analysis and Design of a Compact Modified Delta Parallel Mechanism

Abstract

In our previous work, we developed a compact 6-DOF haptic interface as a master device which achieved an effective manual teleoperation. The haptic interface contains a modified Delta parallel-link positioning mechanism. Parallel mechanisms are usually characterized by a high stiffness, which, however, is reduced by elastic deformations of both parts and bearings. Therefore, to design such a parallel mechanism, we should analyze its structural stiffness, including elastic deformations of both parts and bearings. Then we propose a simple method to analyze structural stiffness in a parallel mechanism using bearings. Our method is based on standard concepts such as static elastic deformations. However, the important aspect of our method is the manner in which we combine these concepts and how we obtain the value of the elasticity coefficient of a rotation axis in a bearing. Finally, we design a modified Delta mechanism, with a well-balanced stiffness, based on our method of stiffness analysis.

Elasto-geometrical modeling and calibration of redundantly actuated PKMs

“…The small and high stiffness coefficients must be chosen so that they are as far as possible from the other stiffness coefficients and that the numerical accuracy is still valid. A drawback of this solution, called penalty method, is that the setting of these stiffness values is difficult because it must be a compromise between computational instability and results accuracy [21]. Its advantages reside in the ease of implementation and in particular the fact that its associated matrix is positive definite.…”

Indices for Stiffness and Singularity Evaluation for Designing 5R Parallel Manipulators

“…The input angles θ 1 and θ 2 can be obtained by using the inverse kinematic, when the position of point P is known by considering the following restriction: 2 r pb i = , i = 1,2 (14) or in the scalar form (16) If the output point P is known, the inputs angles for reaching this position can be obtained as…”

“…These objectives are in conflict with each other, mainly in the applications where the robot should work at high velocities. Therefore, the study of the stiffness becomes of primary importance to design multibody robotic systems in order to properly choose materials, geometry components, shape and size, interaction of components with each other, mechanical transmission of mechanisms, actuators and the controller [12,15,16].…”

Kinematically Redundant Parallel Haptic Device with Large Workspace

“…In order to further increase force reflection and stiffness, parallel-kinematic manipulators have been employed as haptic device mechanisms [9][10][11][12][13][14]. One of the most famous parallel-type haptic devices may be Delta haptics [15][16][17][18]. The Delta parallel manipulator has large force reflection and high stiffness due to parallel structure and parallelogram.…”