The elliptic integral solution is often considered to be the most accurate method for analyzing large deflections of thin beams in compliant mechanisms. In this paper, a comprehensive solution based on the elliptic integrals is proposed for solving large deflection problems. By explicitly incorporating the number of inflection points and the sign of the end-moment load in the derivation, the comprehensive solution is capable of solving large deflections of thin beams with multiple inflection points and subject to any kinds of load cases. The comprehensive solution also extends the elliptic integral solutions to be suitable for any beam end angle. Deflected configurations of complex modes solved by the comprehensive solution are presented and discussed. The use of the comprehensive solution in analyzing compliant mechanisms is also demonstrated by examples.

A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms

Modeling Large Planar Deflections of Flexible Beams in Compliant Mechanisms Using Chained Beam-Constraint-Model

Design of a flexure-based constant-force XY precision positioning stage

\n Flexure-based compliant mechanisms are becoming increasingly promising in precision engineering, robotics, and other applications due to the excellent advantages of no friction, no backlash, no wear, and minimal requirement of assembly. Because compliant mechanisms have inherent coupling of kinematic-mechanical behaviors with large deflections and/or complex serial-parallel configurations, the kinetostatic and dynamic analyses are challenging in comparison to their rigid-body counterparts. To address these challenges, a variety of techniques have been reported in a growing stream of publications. This paper surveys and compares the conceptual ideas, key advances, and applicable scopes, and open problems of the state-of-the-art kinetostatic and dynamic modeling methods for compliant mechanisms in terms of small and large deflections. Future challenges are discussed and new opportunities for extended study are highlighted as well. The presented review provides a guide on how to select suitable modeling approaches for those engaged in the field of compliant mechanisms.

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Kinetostatic and Dynamic Modeling of Flexure-Based Compliant Mechanisms: A Survey

Force regulation is a challenging problem for robot end-effectors when interacting with an unknown environment. It often requires sophisticated sensors with computerized control. This paper presents an adjustable constant-force mechanism (ACFM) to passively regulate the contact force of a robot end-effector. The proposed ACFM combines the negative stiffness of a bistable mechanism and positive stiffness of a linear spring to generate a constant-force output. Through prestressing the linear spring, the constant-force magnitude can be adjusted to adapt to different working environments. The ACFM is a monolithic compliant mechanism that has no frictional wear and is capable of miniaturization. We propose a design formulation to find optimal mechanism configurations that produce the most constant-force. A resulting force to displacement curve and maximal stress curve can be easily manipulated to fit a different application requirement. Illustrated experiments show that an end-effector equipped with the ACFM can adapt to a surface of variable height, without additional motion programming. Since sensors and control effort are minimized, we expect this mechanism can provide a reliable alternative for robot end-effectors to interact friendly with an environment.

An Adjustable Constant-Force Mechanism for Adaptive End-Effector Operations

A compliant multistable mechanism is capable of steadily staying at multiple distinct positions without power input. Many applications including switches, valves, relays, positioners, and reconfigurable robots may benefit from multistability. In this paper, two new approaches for synthesizing compliant multistable mechanisms are proposed, which enable designers to achieve multistability through the use of a single bistable mechanism. The synthesis approaches are described and illustrated by several design examples. Compound use of both approaches is also discussed. The design potential of the synthesis approaches is demonstrated by the successful operation of several instantiations of designs that exhibit three, four, five, and nine stable equilibrium positions, respectively. The equations for determining the actuation force required to move a multistable mechanism are provided. The synthesis approaches enable us to design a compliant mechanism with a desired number of stable positions.

Synthesis of Compliant Multistable Mechanisms Through Use of a Single Bistable Mechanism

The pseudo-rigid-body model (PRBM) method has been widely accepted as one of the most important tools for synthesis and analysis of compliant mechanisms. However, the lack of quantitative study on the accuracy of PRBM for predicting the kinetostatic behavior of flexible members always makes users feel unconfident in the results achieved by PRBM. In this paper, a strain-energy-based approach is proposed for evaluating the accuracy of PRBM for predicting kinetostatic behavior of flexible segments, which compares the results of strain energy calculate using PRBM to those obtained using the derived closed-form solutions. The approach was used to evaluate the accuracy of the PRBM for flexible cantilever beams. It is proved that the PRBM is accurate for modeling segments subject to end-moment loads. A thorough comparison for segments subject to end-force loads is also presented. The results could be useful for PRBM users to assess the accuracy of the models for their compliant mechanism designs, or to choose appropriate values for the characteristic parameters. The results may also be used to improve the PRBM.Copyright © 2011 by ASME

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Accuracy Evaluation of PRBM for Predicting Kinetostatic Behavior of Flexible Segments in Compliant Mechanisms

A compliant multistable mechanism is capable of steadily staying at multiple distinct positions without power input. Many applications including switches, valves, relays, positioners, and reconfigurable robots may benefit from multistability. In this paper, two new approaches for synthesizing compliant multistable mechanisms are proposed, which enable designers to achieve multistability through the use of a single bistable mechanism. The synthesis approaches are described and illustrated by several design examples. Compound use of both approaches is also discussed. The design potential of the synthesis approaches is demonstrated by the successful operation of several instantiations of designs that exhibit three, four, five, and nine stable equilibrium positions, respectively. The synthesis approaches enable us to design a compliant mechanism with a desired number of stable positions.Copyright © 2010 by ASME

Aimei Zhang

Papers

A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms

Synthesis of Compliant Multistable Mechanisms Through Use of a Single Bistable Mechanism

Accuracy Evaluation of PRBM for Predicting Kinetostatic Behavior of Flexible Segments in Compliant Mechanisms

Achieving Multistability Through Use of a Single Bistable Compliant Mechanism