A Pseudo-rigid-body Model for Functionally Binary Pinned-pinned Segments Used in Compliant Mechanisms
نویسندگان
چکیده
The pseudo-rigid-body model concept allows compliant mechanisms to be analyzed using well-known rigid-body kinematics. This paper presents a pseudo-rigid-body model for initially circular functionally binary pinned-pinned segments that undergo large, nonlinear deflections. The model approximates the functionally binary pinned-pinned segment as three rigid members joined by pin joints. Torsional springs placed at the joints model the segment’s stiffness. This model has been tested by fabricating several such segments from a variety of different materials. An example mechanism incorporating functionally binary pinned-pinned segments is also presented. INTRODUCTION The nonlinear deflections often associated with the motion of compliant mechanisms increase the complexity of compliant mechanism analysis and design. Though these deflections may be difficult to analyze, they are necessary because many of the advantages of compliant mechanisms result from the reduced part count made possible by obtaining motion from deflections rather than from traditional kinematic pairs (Shoup and McLarnan, 1971; Ananthasuresh and Kota, 1995). Analysis methods must be developed that simplify the analysis of the large-deflection compliant members so that compliant mechanisms may be designed. The pseudo-rigid-body model concept has been developed in response to this need (Howell and Midha, 1994). The pseudo-rigid-body model is used to unify compliant mechanism theory with rigid-body mechanism theory. This is accomplished by replacing a compliant segment with two or more rigid segments joined by a pin joint, with the lengths of the equivalent rigid segments specified so that their motion closely models that of the compliant segments. A torsional spring at the pin joint models the compliant segment’s resistance to bending. This type of model has been applied to small-length flexural segments (Howell and Midha, 1994), initially straight fixed compliant segments with constant end loads (Howell and Midha, 1995), and initially curved segments with similar loads (Howell and Midha, 1996). Other methods exist as alternatives to the pseudo-rigid-body model for the design of compliant mechanisms. For example, structural optimization, homogenization theory, topology optimization, and multi-criteria optimization methods have been proposed for compliant mechanism design (Ananthasuresh and Kota, 1994, Frecker et al., 1997, Sigmund, 1996). A common compliant link that has yet to have a pseudorigid-body model is the functionally binary pinned-pinned segment (FBPP segment), shown schematically in Fig. 1 (Edwards, 1996). Because it is pinned at both ends, the segment cannot carry moments or vertical loads; it is limited to horizontal loading. Because of this required loading, the segment behaves much like a simple linear spring. However, its force-deflection characteristics are not linear, and they depend to a large extent on the parameters of the FBPP segment. This paper presents a model for finding the force and moment characteristics of segments whose undeflected shape is a circular arc, as shown in 1 Copyright © 1999 by ASME Fig. 2. This segment is often used in compliant mechanisms because of its simple geometry. For example, the mechanism illustrated schematically in Fig. 3 uses a functionally binary pinned-pinned segment to allow motion. The model presented in this paper will allow this motion to be analyzed using rigid-body kinematics. Before analyzing the segment shown in Fig. 2, the problem can be simplified by realizing that the segment is symmetric about a vertical line through its center. This symmetry can be used to divide the complete FBPP segment into two equivalent half-segments. One such half-segment is shown in Fig. 4. This segment will be analyzed, and the results will be generalized to the full segment. The following sections show how this may be done. ELLIPTIC INTEGRAL SOLUTION The large-scale force-deflection relationships for functionally binary pinned-pinned (FBPP) segments require some form of a nonlinear solution. The classical method for determining these values has been through the use of elliptic integrals, which provide a means for solving the nonlinear equations (Bisshopp and Drucker, 1945; Frisch-Fay, 1962). Elliptic integrals are any of a wide range of non-elementary integrals which are intractable and have no elementary solution (Byrd and Friedman, 1954). Integrals which can be manipulated to conform to an elliptic integral basic function can then be transformed into an elliptic integral solution. These solutions may be evaluated using methods such as Landen’s scale of increasing amplitudes, which uses Gauss’ Arithmetico-Geometrical Means (King, 1924). Upon deflection, the FBPP segment assumes an unknown shape which varies based on initial curvature, material properties, and applied force. The curvature of the half-segment may be found using the Bernoulli-Euler equation:
منابع مشابه
Combinatorial Rigidity and Independence of Generalized Pinned Subspace-Incidence Constraint Systems
Given a hypergraph H with m hyperedges and a set X of m pins, i.e. globally fixed subspaces in Euclidean space R, a pinned subspaceincidence system is the pair (H,X), with the constraint that each pin in X lies on the subspace spanned by the point realizations in R of vertices of the corresponding hyperedge of H . We are interested in combinatorial characterization of pinned subspace-incidence ...
متن کاملSeismic Reliability Analysis of Offshore Fixed Platforms Using Incremental Dynamic Analysis
It is generally accepted that performance-based design has to be reliability-based. Seismic performance evaluation is based on nonlinear dynamics and reliability theory taking into account uncertainties during analysis. Considering the economic importance of jacket type offshore platforms, the present research aims to assess the seismic performance of offshore steel platforms. In this study, th...
متن کاملTransverse Vibration for Non-uniform Timoshenko Nano-beams
In this paper, Eringen’s nonlocal elasticity and Timoshenko beam theories are implemented to analyze the bending vibration for non-uniform nano-beams. The governing equations and the boundary conditions are derived using Hamilton’s principle. A Generalized Differential Quadrature Method (GDQM) is utilized for solving the governing equations of non-uniform Timoshenko nano-beam for pinned-pinned...
متن کاملOn the Design Methodology of Flexure-Based Compliant Mechanisms by Utilizing Pseudo-Rigid-Body Models with 3-DOF Joints
This paper focuses on the complex design process of planar compliant mechanisms with flexure hinges. In the following a systematic methodology of the transition from lever mechanisms generated intuitively by the developer or non-intuitively by topology optimization to applicable compliant mechanism is presented. An extended pseudo-rigid-body model (PRBM) is used for the analysis and the modific...
متن کاملDynamic Simulation of A Large Deployable Space Structure with Pinned Joints
Plays of joints strongly influence the dynamics of the large deployable space structures. In this paper, dynamic simulation of space structures with pinned joints is discussed. The study can be simply divided into two parts: the flexible effect of structure is simulated by MSC/NASTRAN, and the global motion of rigid body by DADS. The details of how to select the deformation modes in MSC/NASTRAN...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999