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 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.

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.

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.

Estimating Optimized Stress Bounds in Early Stage Design of Compliant Mechanisms

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Sree Kalyan Patiballa ◽  
Girish Krishnan
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Early Stage ◽  
Functional Characterization ◽  
Stress Constraints ◽  
Design Synthesis ◽  
Stage Design ◽  
Computationally Intensive ◽  
Early Stage Design ◽  
Selection Of

Design synthesis of distributed compliant mechanisms is often a two-stage process involving (a) conceptual topology synthesis and a subsequent (b) refinement stage to meet strength and manufacturing specifications. The usefulness of a solution is ascertained only after the sequential completion of these two steps that are, in general, computationally intensive. This paper presents a strategy to rapidly estimate final operating stresses even before the actual refinement process. This strategy is based on the uniform stress distribution metric, and a functional characterization of the different members that constitute the compliant mechanism topology. Furthermore, this paper uses the underlying mechanics of stress bound estimation to propose two rule of thumb guidelines for insightful selection of topologies and systematically modifying them for an application. The selection of the best conceptual solution in the early stage design avoids refinement of topologies that inherently may not meet the stress constraints. This paper presents two examples that illustrate these guidelines through the selection and refinement of topologies for a planar compliant gripper application.

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

1996 ◽  
Vol 118 (1) ◽  
pp. 126-131 ◽  
Author(s):  
L. L. Howell ◽  
A. Midha ◽  
T. W. Norton
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Spring Stiffness ◽  
Model Concept ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Body Joints

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. 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.

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.

A Method for a More Accurate Calculation of the Stiffness Coefficient in a Pseudo-Rigid-Body Model (PRBM) of a Fixed-Free Beam Subjected to End Forces

2014 ◽  
Author(s):  
Ashok Midha ◽  
Raghvendra S. Kuber ◽  
Vivekananda Chinta ◽  
Sushrut G. Bapat
Keyword(s):  
Rigid Body ◽  
Inflection Point ◽  
Compliant Mechanisms ◽  
Load Factor ◽  
Stiffness Coefficient ◽  
Body Angle ◽  
Analysis And Design ◽  
Body Model ◽  
Body Parameter ◽  
Rigid Body Model

The pseudo-rigid-body model (PRBM) concept allows compliant mechanisms to be modeled using existing knowledge of rigid-body mechanisms, thereby considerably simplifying their analysis and design. The PRBMs represent the compliant segments with two or more rigid-body segments, connected using pin joints (characteristic pivots). The beam compliance is modeled using a torsional spring placed at the characteristic pivot, whose spring constant K is evaluated using a pseudo-rigid-body parameter termed as the beam stiffness coefficient. This paper presents a method to more accurately calculate the beam stiffness coefficient for a fixed-free compliant beam subjected to a combination of horizontal and vertical forces. The improved stiffness coefficient (KΘ) expressions are derived as a function of the pseudo-rigid-body angle, Θ and the load factor, n. To exemplify the application of the improved results, the expressions derived are successfully implemented in modeling a fixed-guided beam with an inflection point, allowing it to be modeled as two fixed-free beams pinned at the inflection point.

Large-Deflection Analysis of General Beams in Contact-Aided Compliant Mechanisms Using Chained Pseudo-Rigid-Body Model

2020 ◽  
Vol 12 (3) ◽  
Author(s):  
Mohui Jin ◽  
Zhou Yang ◽  
Collin Ynchausti ◽  
Benliang Zhu ◽  
Xianmin Zhang ◽  
...  
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Reaction Force ◽  
Curved Beams ◽  
Nonlinear Method ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Force Moment

Abstract The nonlinear analysis and design of contact-aided compliant mechanisms (CCMs) are challenging. This paper presents a nonlinear method for analyzing the deformation of general beams that contact rigid surfaces in CCMs. The large deflection of the general beam is modeled by using the chained pseudo-rigid-body model. A geometry constraint from the contact surface is developed to constrain the beam’s deformed configuration. The contact analysis problem is formulated based on the principle of minimum potential energy and solved using an optimization algorithm. Besides, a novel technique based on the principle of work and energy is proposed to calculate the reaction force/moment of displacement-loaded cases. Several analysis examples of the compliant mechanisms with straight or curved beams are used to verify the proposed method. The results show that the proposed method and technique can evaluate the deformation of beam-based CCMs and the reaction force/moment with acceptable accuracy, respectively.

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