Pseudo-Rigid Body Dynamic Modeling of Compliant Members for Design

2019 ◽  
Author(s):  
Vedant ◽  
James T. Allison
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Flexible Beam ◽  
Finite Element Models ◽  
Structural Members ◽  
Resonant Frequencies ◽  
Design Studies ◽  
Rigid Body Dynamic ◽  
Revolute Joints ◽  
Body Dynamic

Abstract Movement in compliant mechanisms is achieved, at least in part, via deformable flexible members, rather than using articulating joints. These flexible members are traditionally modeled using Finite Element Models (FEMs). In this article, an alternative strategy for modeling compliant cantilever beams is developed with the objectives of reducing computational expense, and providing accuracy with respect to design optimization solutions. The method involves approximating the response of a flexible beam with an n-link/m-joint Pseudo-Rigid Body Dynamic Model (PRBDM). Traditionally, PRBDM models have shown an approximation of compliant elements using 2 or 3 revolute joints (2R/3R-PRBDM). In this study, a more general nR-PRBDM model is developed. The first n resonant frequencies of the PRBDM are matched to exact or FEM solutions to approximate the response of the compliant system. These models can be used for co-design studies of flexible structural members, and are capable of modeling higher deflection of compliant elements.

Pseudo-Rigid-Body Dynamic Models for Design of Compliant Members

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Vedant ◽  
James T. Allison
Keyword(s):  
Rigid Body ◽  
Dynamic Models ◽  
Compliant Mechanisms ◽  
Flexible Beam ◽  
Dynamical Response ◽  
Structural Members ◽  
Element Analysis ◽  
Rigid Body Dynamic ◽  
Revolute Joints ◽  
Body Dynamic

Abstract Movement in compliant mechanisms is achieved, at least in part, via deformable flexible members, rather than using articulating joints. These flexible members are traditionally modeled using finite element analysis (FEA)-based models. In this article, an alternative strategy for modeling compliant cantilever beams is developed with the objectives of reducing computational expense and providing accuracy with respect to design optimization solutions. The method involves approximating the response of a flexible beam with an n-link/m-joint pseudo-rigid-body dynamic model (PRBDM). Traditionally, static pseudo-rigid-body models (PRBMs) have shown an approximation of compliant elements using two or three revolute joints (2R/3R-PRBM). In this study, a more general nR-PRBDM model is developed. The first n resonant frequencies of the PRBDM are matched to exact or FEA solutions to approximate the response of the compliant system and compared with existing PRBMs. PRBDMs can be used for co-design studies of flexible structural members and are capable of modeling large deflections of compliant elements. We demonstrate PRBDMs that show dynamically accurate response for a random geometry cantilever beam by matching the steady-state and frequency response, with dynamical response accuracies up to 10% using a 5R-PRBDM.

Pseudo-rigid-body dynamic modeling and analysis of compliant mechanisms

2017 ◽  
Vol 232 (9) ◽  
pp. 1665-1678 ◽  
Author(s):  
Yue-Qing Yu ◽  
Qian Li ◽  
Qi-Ping Xu
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Dynamic Models ◽  
Compliant Mechanisms ◽  
Lagrange Equation ◽  
Dynamic Responses ◽  
Modeling And Analysis ◽  
Rigid Body Dynamic ◽  
Body Dynamic

An intensive study on the dynamic modeling and analysis of compliant mechanisms is presented in this paper based on the pseudo-rigid-body model. The pseudo-rigid-body dynamic model with single degree-of-freedom is proposed at first and the dynamic equation of the 1R pseudo-rigid-body dynamic model for a flexural beam is presented briefly. The pseudo-rigid-body dynamic models with multi-degrees-of-freedom are then derived in detail. The dynamic equations of the 2R pseudo-rigid-body dynamic model and 3R pseudo-rigid-body dynamic model for the flexural beams are obtained using Lagrange equation. Numerical investigations on the natural frequencies and dynamic responses of the three pseudo-rigid-body dynamic models are made. The effectiveness and superiority of the pseudo-rigid-body dynamic model has been shown by comparing with the finite element analysis method. An example of a compliant parallel-guiding mechanism is presented to investigate the dynamic behavior of the mechanism using the 2R pseudo-rigid-body dynamic model.

Kinematic and dynamic analysis of compliant mechanisms considering both lateral and axial deformations of flexural beams

2018 ◽  
Vol 233 (3) ◽  
pp. 1007-1020 ◽  
Author(s):  
Yue-Qing Yu ◽  
Peng Zhou ◽  
Qi-Ping Xu
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Dynamic Model ◽  
Compliant Mechanisms ◽  
Dynamic Responses ◽  
Flexible Beams ◽  
Rigid Body Dynamic ◽  
Body Model ◽  
Rigid Body Model ◽  
Body Dynamic

The kinematic and dynamic analysis of compliant mechanisms is investigated comprehensively in this work. Based on the pseudo-rigid-body model, a new PR model is proposed to simulate both the lateral and axial deformations of flexural beams in compliant mechanisms. An optimization for the characteristic factors and a linear regression for the stiffness coefficients of PR pseudo-rigid-body model are presented. Compared with the 1R and 2R pseudo-rigid-body model, the advantage of the PR model is well illustrated. The dynamic modeling of flexible beams in compliant mechanisms is then developed based on the PR pseudo-rigid-body model. The dynamic equation of a PR pseudo-rigid-body dynamic model is derived and the dynamic responses are then presented. The kinematic and dynamic analysis of a compliant slider-crank mechanism is presented by the 1R, 2R and PR model, respectively. The effectiveness of pseudo-rigid-body models and the superiorities of the PR pseudo-rigid-body model and PR pseudo-rigid-body dynamic model are shown clearly in the numerical example.

Steady-State Rigid-Body Dynamic Response of Cam-Follower Mechanisms

1994 ◽  
Author(s):  
Andi I. Mahyuddin ◽  
Ashok Midha
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Rigid Body ◽  
Angular Speed ◽  
Integration Scheme ◽  
Rigid Body Dynamic ◽  
Speed Variation ◽  
Cam Follower ◽  
Speed Fluctuation ◽  
Body Dynamic

Abstract The camshaft of a cam-follower mechanism experiences a position-dependent moment due to the force exerted on the cam by the follower, causing the angular speed of the camshaft to fluctuate. In this work, a method to expediently predict the camshaft speed fluctuation is developed. The governing equation of motion is derived assuming that the cam-follower system is an ideal one wherein all members are treated as rigid. An existing closed-form numerical algorithm is used to obtain the steady-state rigid-body dynamic response of a machine system. The solution considers a velocity-dependent moment; specifically, a resisting moment is modeled as a velocity-squared damping. The effects of flywheel size and resisting moment on camshaft speed fluctuation are studied. The results compare favorably with those obtained from transient response using a direct integration scheme. The analytical result also shows excellent agreement with the camshaft speed variation of an experimental cam-follower mechanism. The steady-state rigid-body dynamic response obtained herein also serves as a first approximation to the input camshaft speed variation in the dynamic analysis of flexible cam-follower mechanisms in a subsequent research.

Kinematic Synthesis of Planar, Shape-Changing Compliant Mechanisms Using Pseudo-Rigid-Body Models

2012 ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Rigid Body ◽  
Shape Matching ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Flexible Beam ◽  
Beam Model ◽  
Flexible Beams ◽  
Multi Objective Genetic Algorithm ◽  
Optimization Loop

This paper presents a procedure using Pseudo-Rigid-Body Models (PRBMs) to synthesize partially compliant mechanisms capable of approximating a shape change defined by a set of morphing curves in different positions. To generate a single-piece compliant mechanism, flexural pivots and flexible beams are both utilized in the mechanism. New topologies defined by compliant mechanism matrices are enumerated by modifying the components that make up a single degree-of-freedom (DOF) rigid-body mechanism. Because of the introduction of the PRBM for flexural pivots and the simplified PRBM for flexible beams, torsional springs are attached at the characteristic pivots of the 1-DOF rigid-body mechanism in order to generate a corresponding pseudo-rigid-body mechanism. A multi-objective genetic algorithm is employed to find a group of viable compliant mechanisms in the form of candidate pseudo-rigid-body mechanisms that tradeoff minimizing shape matching error with minimizing actuator energy. Since the simplified beam model is not accurate, an optimization loop is established to find the position and shape of the flexible beam using a finite link beam model. The optimal flexible beams together with the pseudo-rigid-body mechanism define the solution mechanism. The procedure is demonstrated with an example in which a partially compliant mechanism approximating two closed-curve profiles is synthesized.

SPHERE ENCAPSULATED ORIENTED-DISCRETE ORIENTATION POLYTOPES (S-DOP) COLLISION CULLING FOR MULTI-, RIGID BODY DYNAMIC

2015 ◽  
Vol 75 (2) ◽  
Author(s):  
Norhaida Mohd Suaib ◽  
Abdullah Bade ◽  
Dzulkifli Mohamad
Keyword(s):  
Rigid Body ◽  
Collision Detection ◽  
Simulation System ◽  
Improve Performance ◽  
Excellent Performance ◽  
Approximation Techniques ◽  
Rigid Body Dynamic ◽  
Rigid Body Simulation ◽  
Body Dynamic

This paper discusses on sphere encapsulated oriented-discrete orientation polytopes (therefore will be referred to as S-Dop) collision culling for multiple rigid body simulation. In order to improve performance of the whole simulation system, there are available options in sacrificing the accuracy over speed by using certain approximation techniques. The aim of this research is to achieve excellent performance through implementation of suitable culling technique, without jeopardizing the resulting behavior so that the simulation will still be physically plausible. The basic idea is to identify the highly probable pairs to collide and test the pair with a more accurate collision test in broad-phase collision detection, before the pair is passed to a more costly stage. Results from the experiments showed that there are a number of ways to implement the sphere encapsulated or-Dops (S-Dop) collision culling on a multiple rigid body simulation depending on the level of performance needed.  

Compliant Wireform Mechanisms

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Tyler M. Pendleton ◽  
Brian D. Jensen
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Finite Element Models ◽  
Simplified Models ◽  
New Class ◽  
Body Model ◽  
Single Piece ◽  
Rigid Body Model ◽  
Torsion Springs ◽  
Torsion Bar

This paper presents an alternative to fabrication methods commonly used in compliant mechanisms research, resulting in a new class of compliant mechanisms called wireform mechanisms. This technique integrates torsional springs made of formed wire into compliant mechanisms. In this way the desired force, stiffness, and motion can be achieved from a single piece of formed wire. Two techniques of integrating torsion springs are fabricated and modeled: helical coil torsion springs and torsion bars. Because the mechanisms are more complex than ordinary springs, simplified models, which aid in design, are presented, which represent the wireform mechanisms as rigid-body mechanisms using the pseudo-rigid-body model. The method is demonstrated through the design of a mechanically tristable mechanism. The validity of the simplified models is discussed by comparison to finite element models and, in the case of the torsion-bar mechanism, to experimental measurements.

Sign in / Sign up

Export Citation Format

Share Document