scholarly journals A Versatile 3R Pseudo-Rigid-Body Model for Initially Curved and Straight Compliant Beams of Uniform Cross Section

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Venkatasubramanian Kalpathy Venkiteswaran ◽  
Hai-Jun Su
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Element Analysis ◽  
Revolute Joints ◽  
Rigid Body Model ◽  
Uniform Cross Section ◽  
Optimized Model ◽  
Force Mechanism ◽  
Parameter Values ◽  
Constant Force Mechanism

Rigid-body discretization of continuum elements was developed as a method for simplifying the kinematics of otherwise complex systems. Recent work on pseudo-rigid-body (PRB) models for compliant mechanisms has opened up the possibility of using similar concepts for synthesis and design, while incorporating various types of flexible elements within the same framework. In this paper, an idea for combining initially curved and straight beams within planar compliant mechanisms is developed to create a set of equations that can be used to analyze various designs and topologies. A PRB model with three revolute joints is derived to approximate the behavior of initially curved compliant beams, while treating straight beams as a special case (zero curvature). The optimized model parameter values are tabled for a range of arc angles. The general kinematic and static equations for a single-loop mechanism are shown, with an example to illustrate accuracy for shape and displacement . Finally, this framework is used for the design of a compliant constant force mechanism to illustrate its application, and comparisons with finite element analysis (FEA) are provided for validation.

Pseudo-Rigid-Body Models of Initially-Curved and Straight Beams for Designing Compliant Mechanisms

2017 ◽  
Author(s):  
Venkatasubramanian Kalpathy Venkiteswaran ◽  
Hai-Jun Su
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Early Stage ◽  
Element Analysis ◽  
Stage Design ◽  
Analysis And Design ◽  
Revolute Joints ◽  
Rigid Body Model ◽  
Early Stage Design ◽  
Force Mechanism

The use of pseudo-rigid-body models in the analysis and design of compliant mechanisms has opened up the possibility of using various types of flexible elements within the same framework. In this paper, an idea for combining initially curved and straight beams within compliant mechanisms is developed to create a set of equations that can be easily used to analyze various designs and topologies. A pseudo-rigid-body model with three revolute joints is derived to approximate the behavior of initially-curved compliant beams, to go with another model previously presented for straight beams. The general kinematic and static equations for a single-loop mechanism are shown. Finally, this setup is used for the early-stage design of a compliant constant force mechanism to illustrate its application and comparisons with Finite Element Analysis for validation.

scholarly journals Compliant Mechanism Road Bicycle Brake: A Rigid-Body Replacement Case Study

2011 ◽  
Author(s):  
Brian M. Olsen ◽  
Larry L. Howell ◽  
Spencer P. Magleby
Keyword(s):  
Rigid Body ◽  
High Performance ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Element Analysis ◽  
Low Weight ◽  
Rigid Body Model ◽  
Compliant Mechanism Design

This paper demonstrates rigid-body replacement synthesis in the design a mechanism with known design objectives. The design of high-performance bicycle brakes is complicated by a variety of competing design objectives, including increased performance and low weight. But this challenge also provides a good case study to demonstrate the design of compliant mechanisms to replace traditional rigid-link mechanisms. This paper briefly reviews current road brake designs, demonstrates the use of rigid-body replacement synthesis to design a compliant mechanism, and illustrates the combination of compliant mechanism design tools. The resulting concept was generated from the modified dual-pivot brake design and is a partially compliant mechanism where one pin has the dual role of a joint and a mounting pin. The pseudo-rigid-body model, finite element analysis, and optimization algorithms are used to generate design dimensions, and designs are considered for both titanium and E-glass flexures. The resulting design has the potential of reducing the part count and overall weight while maintaining a performance similar to the benchmark.

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.

scholarly journals Adaptive pseudo-rigid-body model for generalized cross-spring pivots under combined loads

2020 ◽  
Vol 12 (12) ◽  
pp. 168781402096653
Author(s):  
Zhongzhou Wang ◽  
Haixuan Sun ◽  
Bidou Wang ◽  
Peng Wang
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Parametric Design ◽  
Optimization Techniques ◽  
Characteristic Analysis ◽  
Element Analysis ◽  
Combined Loads ◽  
Rigid Body Model ◽  
Instantaneous Center ◽  
Constraint Model

Generalized cross-spring pivots (CSPs) are widely used as revolute joints in precision machinery. However, pseudo-rigid-body (PRB) models cannot capture the parasitic motions of a generalized CSP exactly under combined loads; moreover, the characteristic parameters used in PRB methods must be recomputed using optimization techniques. In this study, we develop two simple and accurate PRB models for generalized CSPs. First, a PRB method for a beam is developed based on the beam constraint model and the instantaneous center model, where the beam is modeled as two rigid links joined at a pivot via a torsion spring. Subsequently, two PRB models of the generalized CSP, comprising a four-bar model for accuracy and a pin-joint model for stiffness, are constructed based on a kinematic analysis using the proposed PRB method. A deflection characteristic analysis is then conducted to determine the relationship between the proposed model and the existing models. Finally, the PRB models for the pivot under the action of combined loads are validated via finite element analysis. The error evaluation indicates that the proposed PRB models are more accurate than the results from existing methods. The PRB models proposed here can be used in parametric design of compliant mechanisms.

Dimensional Synthesis of Compliant Constant-Force Slider Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha ◽  
Morgan D. Murphy
Keyword(s):  
Compliant Mechanisms ◽  
Design Procedure ◽  
Constant Force ◽  
Dimensional Synthesis ◽  
Model Concept ◽  
Output Force ◽  
Rigid Body Model ◽  
Constant Output ◽  
Force Mechanism ◽  
Constant Force Mechanism

Abstract Constant-force mechanisms produce a constant output force for a range of input displacements. Such mechanisms are important in applications with a varying displacement but a constant resultant force required. Constant-force mechanism designs have been limited to rigid-link mechanisms, but the design of compliant, or flexible link, constant force mechanisms could increase the number of applications by taking advantage of the unique characteristics of compliant mechanisms. Murphy (1993) developed type-synthesis theories for compliant mechanisms and applied them to generate possible configurations for compliant constant-force slider mechanisms. This paper concentrates on the dimensional synthesis of several of the resulting topologies. Optimization and the pseudo-rigid-body-model concept are employed in the design procedure. An example application as an electrical connection for use in electronic chip carriers is also illustrated.

scholarly journals A Preliminary Study on the Compliant Stretcher Mechanism of Canopy

2021 ◽  
Vol 243 ◽  
pp. 02007
Author(s):  
Sara Lee Kit Yee ◽  
Lam Yeap Sheng ◽  
Tan Yong Li
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Element Analysis ◽  
Kinematic Synthesis ◽  
Rigid Body Model ◽  
Reference Design ◽  
Fea Simulation ◽  
Short Product ◽  
Rigid Joints ◽  
Monolithic Structure

The design of the canopy utilizes the conventional rigid body mechanisms which is vulnerable to the presence of backlash, friction of joints or wearing of mechanical parts which lead to short product life. Compliant mechanisms are employed to reduce these mechanical problems, owing to their zero-joint and monolithic structure. A reference design for the conventional canopy was chosen and modified through reviewing different patent designs. Six different configurations of the pseudo-rigid-body model (PRBM) were constructed, and the best configuration was selected. Kinematic synthesis with function generation was performed for the chosen PRBM using MATLAB. The obtained results from the kinematic synthesis were then used to calculate the dimensions and stresses of the flexural pivots for the compliant stretcher mechanism. Finite Element Analysis (FEA) simulation was then performed on each of the models and the obtained flexural pivot stresses were compared with that of the PRBM. This research successfully replaces all the rigid joints and links of the stretcher mechanism of the conventional canopy to form a monolithic structure of compliant stretcher mechanism.

A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments

1998 ◽  
Vol 120 (3) ◽  
pp. 392-400 ◽  
Author(s):  
A. Saxena ◽  
S. N. Kramer
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Elliptic Integral ◽  
Beam Equation ◽  
Large Deflections ◽  
Euler Beam ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads. Because of this fact, traditional methods of deflection analysis do not apply. Since the nonlinearities introduced by these large deflections make the system comprising such members difficult to solve, parametric deflection approximations are deemed helpful in the analysis and synthesis of compliant mechanisms. This is accomplished by representing the compliant mechanism as a pseudo-rigid-body model. A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms. In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads. A numerical integration technique using quadrature formulae has been employed to solve the large deflection Bernoulli-Euler beam equation for the tip deflection. Implementation of this scheme is simpler than the elliptic integral formulation and provides very accurate results. An example for the synthesis of a compliant mechanism using the proposed model is also presented.

A Simple and Accurate Method for Determining Large Deflections in Complaint Mechanisms Subjected to End Forces and Moments

1998 ◽  
Author(s):  
A. Saxena ◽  
Steven N. Kramer
Keyword(s):  
Rigid Body ◽  
Numerical Integration ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Beam Equation ◽  
Integration Scheme ◽  
Large Deflections ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Abstract Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads for which, traditional methods of deflection analysis do not apply Nonlinearities introduced by these large deflections make the system comprising such members difficult to solve Parametric deflection approximations are then deemed helpful in the analysis and synthesis of compliant mechanisms This is accomplished by seeking the pseudo-rigid-body model representation of the compliant mechanism A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads with positive end moments A numerical integration technique using quadrature formulae has been employed to solve the nonlinear Bernoulli-Euler beam equation for the tip deflection Implementation of this scheme is relatively simpler than the elliptic integral formulation and provides nearly accurate results Results of the numerical integration scheme are compared with the beam finite element analysis An example for the synthesis of a compliant mechanism using the proposed model is also presented.

Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Spring Stiffness ◽  
Model Concept ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Body Joints

Abstract Compliant mechanisms gain some or all of their mobility from the flexibility of their members rather than from rigid-body joints only. More efficient and usable analysis and design techniques are needed before the advantages of compliant mechanisms can be fully utilized. In an earlier work, a pseudo-rigid-body model concept, corresponding to an end-loaded geometrically nonlinear, large-deflection beam, was developed to help fulfill this need. In this paper, the pseudo-rigid-body equivalent spring stiffness is investigated and new modeling equations are proposed. The result is a simplified method of modeling the force/deflection relationships of large-deflection members in compliant mechanisms. Flexible segments which maintain a constant end angle are discussed, and an example mechanism is analyzed. The resulting models are valuable in the visualization of the motion of large-deflection systems, as well as the quick and efficient evaluation and optimization of compliant mechanism designs.

Parametric Deflection Approximations for Initially Curved, Large-Deflection Beams in Compliant Mechanisms

1996 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Curved Beam ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Fundamental Type ◽  
Applied Forces ◽  
Flexible Member

Abstract The analysis of systems containing highly flexible members is made difficult by the nonlineararities caused by large deflections of the flexible members. The analysis and design of many such systems may be simplified by using pseudo-rigid-body approximations in modeling the flexible members. The pseudo-rigid-body model represents flexible members as rigid links, joined at pin joints with torsional springs. Appropriate values for link lengths and torsional spring stiffnesses are determined such that the deflection path and force-deflection relationships are modeled accurately. Pseudo-rigid-body approximations have been developed for initially straight beams with externally applied forces at the beam end. This work develops approximations for another fundamental type of flexible member, the initially curved beam with applied force at the beam end. This type of flexible member is commonly used in compliant mechanisms. An example of the use of the resulting pseudo-rigid-body approximations in compliant mechanisms is included.

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