Synthesis of Compliant Mechanisms With Specified Equilibrium Positions

2005 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Compliant Mechanisms ◽  
Equilibrium Constraints ◽  
Equilibrium Equations ◽  
Equilibrium Configurations ◽  
Form Design ◽  
Design Requirements ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Sine And Cosine Functions

This paper presents a synthesis procedure for a compliant four-bar linkage with three specified equilibrium configurations. The finite position synthesis equations are combined with equilibrium constraints at the flexure pivots to form design equations. These equations are simplified by modeling the joint angle variables in the equilibrium equations using sine and cosine functions. Solutions to these design equations were computed using a polynomial homotopy solver. In order to provide a design specification, we first compute the six equilibrium configurations of a known compliant four-bar mechanism. We use these results as design requirements to synthesize a compliant four-bar. The solver obtained eight real solutions which we refined using a Newton-Raphson technique. A numerical example is provided to verify the design methodology.

Synthesis of Bistable Compliant Four-Bar Mechanisms Using Polynomial Homotopy

2006 ◽  
Vol 129 (10) ◽  
pp. 1094-1098 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Compliant Mechanisms ◽  
Homotopy Continuation ◽  
Equilibrium Constraints ◽  
Equilibrium Equations ◽  
Kinematic Synthesis ◽  
Equilibrium Configurations ◽  
Form Design ◽  
Four Bar Linkage ◽  
Sine And Cosine Functions ◽  
Cosine Functions

In this paper we formulate and solve the synthesis equations for a compliant four-bar linkage with three specified equilibrium configurations in the plane. The kinematic synthesis equations as for rigid-body mechanisms are combined with equilibrium constraints at the flexure pivots to form design equations. These equations are simplified by modeling the joint angle variables in the equilibrium equations using sine and cosine functions. Polynomial homotopy continuation is applied to compute all of the design candidates that satisfy these design equations, which are refined using a Newton-Raphson technique. A numerical example demonstrates design methodology in which the homotopy solver obtained eight real solutions. Two of them provide two stable and one unstable equilibrium, and hence, can be used as the prototype of bistable compliant mechanisms.

A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms

2005 ◽  
Vol 128 (4) ◽  
pp. 776-786 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Potential Energy ◽  
Static Analysis ◽  
Compliant Mechanisms ◽  
Potential Energy Function ◽  
Equilibrium Equations ◽  
Equilibrium Configurations ◽  
Force Moment ◽  
Four Bar Linkage ◽  
Derivatives Of ◽  
Raphson Iteration

This paper formulates the inverse static analysis of planar compliant mechanisms in polynomial form. The goal is to find the equilibrium configurations of the system in response to a known force/moment applied to the mechanism. The geometric constraint of the linkage defines a set of kinematics equations which are combined with equilibrium equations obtained from partial derivatives of the potential-energy function. In order to apply polynomial homotopy solver to these equations, we approximate the linear torsion spring torque at each joint by using sine and cosine functions. The results obtained from the homotopy solver are then refined using Newton-Raphson iteration. To demonstrate the analysis steps, we study two example planar compliant mechanisms, a four-bar linkage with two torsional springs, and a parallel platform supported by three linear springs. Numerical examples are provided together with plots of the potential energy during a movement between selected equilibrium positions.

Design of Structures With Multiple Equilibrium Configurations

2018 ◽  
Author(s):  
Yang Li ◽  
Sergio Pellegrino
Keyword(s):  
Multiple Equilibrium ◽  
Design Parameters ◽  
Future Research ◽  
Equilibrium Constraints ◽  
Complex Problems ◽  
Equilibrium Configurations ◽  
Four Bar Linkage ◽  
Stable Structures

Being able to design structures with multiple equilibrium configurations is the basis for the design of multi-stable structures, which are of interest for future research on multi-configuration structures that require ‘simple’ actuation schemes. It is already known that adding elastic springs to a rigid mechanism can create structures with multiple equilibrium configurations. The spring properties, such as their rest positions, can be taken as design parameters that can be used to achieve specific equilibrium configurations of the structure. This paper provides a linearized formulation for the equilibrium constraints that can be solved for the rest positions of the springs. This method allows the design of specific equilibrium configurations. It can also handle more complex problems and is easier to solve in comparison to existent techniques. An example design of a four-bar linkage that has 5 equilibrium configurations is presented.

Synthesis of Planar Mechanisms for Coupler Tangent-Line Envelope Generation: An Alternative to Coupler Point-Path Generation

1988 ◽  
Vol 110 (2) ◽  
pp. 122-129 ◽  
Author(s):  
Dev P. Sathyadev ◽  
A. H. Soni
Keyword(s):  
Plane Curve ◽  
Tangent Line ◽  
Path Generation ◽  
Planar Mechanisms ◽  
Novel Approach ◽  
Rigid Body Displacement ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
The Given

A synthesis procedure is developed to envelope a given plane curve by a tangent line carried by the coupler plane of a planar four-bar linkage. The synthesis procedure is based on a modification of the planar rigid-body displacement matrix developed by Suh [1]. The approach is based on considering a given curve as the envelope of a moving tangent line and synthesizing mechanisms to envelope the given curve. This is a novel approach in mechanism design and adds a new dimension to the path-generation problem of mechanism synthesis. The foregoing procedure is also extended to synthesize eight-link mechanisms to simultaneously coordinate the motion of two tangent lines. In addition to finite position synthesis, both infinitesimal and mixed position synthesis are considered.

Synthesis of Distributed Compliant Mechanisms for Adaptive Structures Application: An Elasto-Kinematic Approach

1997 ◽  
Author(s):  
Laxminarayana Saggere ◽  
Sridhar Kota
Keyword(s):  
Smart Materials ◽  
High Performance ◽  
Compliant Mechanisms ◽  
Shape Change ◽  
Current Trend ◽  
Adaptive Structures ◽  
Topology Generation ◽  
Synthesis Procedure ◽  
Actuation Scheme ◽  
Kinematic Approach

Abstract Compliant mechanisms are a class of mechanisms that achieve desired force and motion transmission tasks by undergoing elastic deformations as opposed to rigid-body displacements in the conventional rigid-link mechanisms. Most of the previously reported synthesis studies in compliant mechanisms related to either partially-compliant mechanisms or fully-compliant mechanisms with joint compliance. Methods developed for fully-compliant mechanisms with link compliance addressed the issue of topology generation for desired deflections at discrete points on the mechanism. This paper presents a new, first-principles based synthesis procedure for fully-compliant mechanisms with link compliance — that is, distributed-compliant mechanisms — for continuous shape change requirements in a particular segment of a mechanism. The general approach presented in this paper for the synthesis of distributed compliant mechanisms is shown to be well suited for application in the design of adaptive structures, an emerging class of high-performance structural systems. The current trend in the design of adaptive structures is to embed structures with force or strain inducing “smart” materials to serve as distributed actuators. Potential advantages of using the distributed compliance scheme over the distributed actuation scheme in the design of adaptive structures include a significant reduction in the number of required actuators and controls.

Five Position Synthesis of a Slider-Crank Function Generator

2011 ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Full Range ◽  
Linear Actuator ◽  
Tolerance Zone ◽  
Function Generator ◽  
Front End ◽  
Input And Output ◽  
Function Generators ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Branching Solutions

In this paper, we present a synthesis procedure for the coupler link of a planar slider-crank linkage in order to coordinate input by a linear actuator with the rotation of an output crank. This problem can be formulated in a manner similar to the synthesis of a five position RR coupler link. It is well-known that the resulting equations can produce branching solutions that are not useful. This is addressed by introducing tolerances for the input and output values of the specified task function. The proposed synthesis procedure is then executed on two examples. In the first example, a survey of solutions for tolerance zones of increasing size is conducted. In this example we find that a tolerance zone of 5% of the desired full range results in a number of useful task functions and usable slider-crank function generators. To demonstrate the use of these results, we present an example design for the actuator of the shovel of a front-end loader.

Equilibrium Models of Cities: 1. An Axiomatic Theory

1972 ◽  
Vol 4 (4) ◽  
pp. 429-444 ◽  
Author(s):  
J C Amson
Keyword(s):  
Equations Of State ◽  
Market Equilibrium ◽  
Single Species ◽  
State Equation ◽  
Individual Species ◽  
Axiomatic Theory ◽  
Equilibrium Equations ◽  
Equilibrium Configurations ◽  
Density Relation ◽  
The Individual

A study is undertaken of the concept of a city as an ‘urban gravitational plasma’ consisting of one or more species of civic matter (populations, activity rates, and so on) interacting on themselves and each other, and, at the same time, responding to relocation coercions induced by satisfaction potentials of various kinds (housing rentals, amenity levels, and so on). The latter are assumed to be coupled to the territorial densities of the individual species of civic matter through equations of state, for which the housing rental-population density relation in market equilibrium theory is a prototype. The study is divided into four parts. The first part (presented here) approaches the problem from a formal axiomatic viewpoint, and the axioms and definitions are discussed in relation to the real urban situations from which they are abstracted. The notion of equilibrium configurations for a city is introduced, and the general equilibrium equations necessary for their existence are developed. Three particular illustrations of these equations are offered: that of a single species city, and of a two species city—both with an ideal (polytropic) state equation—and that of a single species city with an imperfect (van der Waals) state equation. These illustrations will be examined in detail in the subsequent three parts of this study.

Kinematic Mapping Based Evaluation of Assembly Modes for Planar Four-Bar Synthesis

2005 ◽  
Author(s):  
Hans-Peter Schro¨cker ◽  
Manfred L. Husty ◽  
J. Michael McCarthy
Keyword(s):  
Image Space ◽  
Synthesis Problem ◽  
New Method ◽  
Kinematic Mapping ◽  
Position Synthesis ◽  
Four Bar Linkage

This paper presents a new method to determine if two task positions used to design a four-bar linkage lie on separate circuits of a coupler curve, known as a “branch defect.” The approach uses the image space of a kinematic mapping to provide a geometric environment for both the synthesis and analysis of four-bar linkages. In contrast to current methods of solution rectification, this approach guides the modification of the specified task positions, which means it can be used for the complete five position synthesis problem.

Design of Compliant Thermal Actuators Using Structural Optimization Based on the Level Set Method

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Takayuki Yamada ◽  
Shintaro Yamasaki ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Structural Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Optimization Method ◽  
Equilibrium Equations ◽  
Thermal Actuators ◽  
Level Set Function ◽  
Initialization Scheme ◽  
Set Function

Compliant mechanisms are designed to be flexible to achieve a specified motion as a mechanism. Such mechanisms can function as compliant thermal actuators in micro-electromechanical systems by intentionally designing configurations that exploit thermal expansion effects in elastic material when appropriate portions of the mechanism structure are heated or are subjected to an electric potential. This paper presents a new structural optimization method for the design of compliant thermal actuators based on the level set method and the finite element method (FEM). First, an optimization problem is formulated that addresses the design of compliant thermal actuators considering the magnitude of the displacement at the output location. Next, the topological derivatives that are used when introducing holes during the optimization process are derived. Based on the optimization formulation, a new structural optimization algorithm is constructed that employs the FEM when solving the equilibrium equations and updating the level set function. The re-initialization of the level set function is performed using a newly developed geometry-based re-initialization scheme. Finally, several design examples are provided to confirm the usefulness of the proposed structural optimization method.

Assembly Variation Analysis of Incompletely Positioned Macpherson Suspension Systems Considering Vehicle Load Change

2020 ◽  
Vol 143 (5) ◽  
Author(s):  
Zhihua Niu ◽  
Sun Jin ◽  
Zhimin Li
Keyword(s):  
Compliant Mechanisms ◽  
Error Rates ◽  
Variation Analysis ◽  
Equilibrium Equations ◽  
Suspension Systems ◽  
Assembly Shop ◽  
Automobile Factory ◽  
Adams Simulation ◽  
Wheel Alignment ◽  
Process Strategy

Abstract The assembly precision of wheel alignment parameters is vital to vehicle handling stability. Due to the vertical wheel displacement and compliant components in suspension systems, it is difficult to assemble qualified vehicles with proper wheel alignment parameters. In the assembly shop of the automobile factory, the adjustment of wheel alignment parameters is the most time-consuming process because it relies on trial and error. In order to provide a theoretical guidance to the precision control of wheel alignment parameters, this paper extends the theory of equilibrium equations of incremental forces (EEIF) to 3D compliant mechanisms. Constraint equations of kinematic joints are adopted to express the spatial relationships of different parts. A couple of fixed and floating joint coordinate systems (CSs) are used together to represent deviations of compliant components. The impacts of suspension part deviations on vertical wheel displacement and assembly deformations are well illustrated by such approach. Accuracy of the proposed method is verified by comparing with ADAMS simulation. The results show that the error rates of the 3D EEIF method are less than 5%. Furthermore, statistical assembly variation analysis of a Macpherson suspension is accomplished by using the proposed method and an optimized process strategy is put forward.

Sign in / Sign up

Export Citation Format

Share Document