A Method of Stiffness Analysis of Parallel Mechanisms

2009 ◽  
pp. 562-570 ◽  
Author(s):  
Boqiang Xu ◽  
Tiemin Li ◽  
Jun Wu
Keyword(s):  
Parallel Mechanisms ◽  
Stiffness Analysis

Stiffness Analysis and Design of a Compact Modified Delta Parallel Mechanism

Robotica ◽  
2004 ◽  
Vol 22 (4) ◽  
pp. 463-475 ◽  
Author(s):  
Woo-Keun Yoon ◽  
Takashi Suehiro ◽  
Yuichi Tsumaki ◽  
Masaru Uchiyama
Keyword(s):  
Parallel Mechanism ◽  
Rotation Axis ◽  
Haptic Interface ◽  
Structural Stiffness ◽  
Parallel Mechanisms ◽  
Simple Method ◽  
Elastic Deformations ◽  
Stiffness Analysis ◽  
Analysis And Design ◽  
Parallel Link

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.

scholarly journals Design and Optimization for a Cardiac Active Stabilizer Based on Planar Parallel Compliant Mechanisms

2012 ◽  
Author(s):  
L. Rubbert ◽  
P. Renaud ◽  
J. Gangloff
Keyword(s):  
Compliant Mechanisms ◽  
Optimization Technique ◽  
Beating Heart ◽  
Parallel Mechanisms ◽  
Stiffness Analysis ◽  
Design And Optimization ◽  
Area Of Interest ◽  
Device Architecture ◽  
Spherical Parallel Mechanism ◽  
High Level

Giving assistance to surgeons during beating heart procedures is currently a great challenge in medical robotics: a high level of safety is required while the beating heart yields high forces and dynamics. In this article, we investigate the design of an active cardiac stabilizer that will provide a motionless area of interest during the surgery. A device architecture is introduced that is based on planar parallel mechanisms. Such mechanisms are particularly interesting for their manufacturing simplicity and compactness. With the considered architecture, spherical compliant joints based on a planar structure need to be designed. Here we present the use of a 3-RRR spherical parallel mechanism. Its kinematic and stiffness analysis are performed using pseudo-rigid body modeling. An optimization of the mechanism is then achieved, using a modified ant colony optimization technique. The achievable performance of this type of compliant spherical joint is then discussed before concluding on the device adequacy with respect to the surgical requirements.

Stiffness synthesis of 3-DOF planar 3RPR parallel mechanisms

Robotica ◽  
2015 ◽  
Vol 34 (12) ◽  
pp. 2776-2787 ◽  
Author(s):  
Kefei Wen ◽  
Chan-Bae Shin ◽  
Tae Won Seo ◽  
Jeh Won Lee
Keyword(s):  
Nonlinear System ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Stiffness Analysis ◽  
Pure Rotation ◽  
Arbitrary Configuration ◽  
Synthesis Strategy ◽  
System Equations ◽  
Three Degree Of Freedom ◽  
Reference Input

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.

Stiffness analysis of cable-driven parallel mechanisms with cables having large sustainable strains

2020 ◽  
Vol 234 (10) ◽  
pp. 1959-1968
Author(s):  
Hao Xiong ◽  
Xiumin Diao
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Sufficient Condition ◽  
Parallel Mechanisms ◽  
Stiffness Analysis ◽  
Six Degrees Of Freedom ◽  
Stiffness Matrices ◽  
Steel Cables ◽  
Isoprene Rubber

A cable-driven parallel mechanism is driven by a group of cables. Cable-driven parallel mechanisms can use various cables (e.g. steel cables, nylon cables, isoprene rubber cables, and extension springs) with different sustainable strains. This paper studies the stiffness of cable-driven parallel mechanisms with cables having large sustainable strains, aiming to achieve significantly adjustable overall stiffness. The overall stiffness of a cable-driven parallel mechanism can be decomposed into the constant base stiffness and the adjustable strain stiffness. This paper proposes and mathematically proves a theorem that guarantees that the overall stiffness of a cable-driven parallel mechanism at an arbitrary stable pose can be dominated by the adjustable strain stiffness when cable strains are larger than 100%. The theorem employs the minimum eigenvalues of stiffness matrices to characterize the stiffness of cable-driven parallel mechanism. The theorem provides a sufficient condition that guarantees that the overall stiffness of a cable-driven parallel mechanism at an arbitrary stable pose can be significantly adjusted (i.e. the adjustable strain stiffness contributes more than the constant base stiffness in determining the overall stiffness). The theorem is verified through the simulation of a cable-driven parallel mechanism with six degrees of freedom and seven cables.

Experimental Validation of Jacobian-Based Stiffness Analysis Method for Parallel Manipulators With Nonredundant Legs

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Antonius G. L. Hoevenaars ◽  
Clément Gosselin ◽  
Patrice Lambert ◽  
Just L. Herder
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Experimental Validation ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Stiffness Analysis ◽  
Levels Of Detail ◽  
Structural Compliance

A complete stiffness analysis of a parallel manipulator considers the structural compliance of all elements, both in designed degrees-of-freedom (DoFs) and constrained DoFs, and also includes the effect of preloading. This paper presents the experimental validation of a Jacobian-based stiffness analysis method for parallel manipulators with nonredundant legs, which considers all those aspects, and which can be applied to limited-DoF parallel manipulators. The experimental validation was performed by comparing differential wrench measurements with predictions based on stiffness analyses with increasing levels of detail. For this purpose, two passive parallel mechanisms were designed, namely, a planar 3DoF mechanism and a spatial 1DoF mechanism. For these mechanisms, it was shown that a stiffness analysis becomes more accurate if preloading and structural compliance are considered.

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