Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications

Abstract

Optimal design methods that use continuum mechanics models are capable of generating suitable topology, shape, and dimensions of compliant mechanisms for desired specifications. Synthesis procedures that use linear elastic finite element models are not quantitatively accurate for large displacement situations. Also, design specifications involving nonlinear force-deflection characteristics and generation of a curved path for the output port cannot be realized with linear models. In this paper, the synthesis of compliant mechanisms is performed using geometrically nonlinear finite element models that appropriately account for large displacements. Frame elements are chosen because of ease of implementation of the general approach and their ability to capture bending deformations. A method for nonlinear design sensitivity analysis is described. Examples are included to illustrate the usefulness of the synthesis method.

On understanding of design problem formulation for compliant mechanisms through topology optimization

“…The third situation can be understood as the nonlinear behaviour of the work-piece. Saxena and Ananthasuresh (2001) designed CMs for path generation, specifying a sequence of input forces, P I1 , P I2 , etc., while two linear springs of constant stiffness along two orthogonal directions were used to model the work-pieces. This is an extension of the DPD for the path generation problem.…”

“…In addition, this model only guarantees the deformation in the desired direction, the deformation in its perpendicular direction is not concerned so that the output port may not pass through the precision points even though the error function is very close to zero. Saxena and Ananthasuresh (2001) designs CMs for path generation (F17) with a sum of least square errors (LSE2) in a x-y coordinate system while the work-piece the CM works with are modeled as linear springs. Precision points in the design domain are described with an x-y coordinates so that the output port needs to traverse through points P i of coordinates (δX * I , δy * i ) with respect to its undeformed position due to input forces.…”

“…With the LSE formulation, one can design CMs for any kinds of output displacement requirements or any kinds of inputoutput relationships. For example, one can design CMs for linear or nonlinear input-output relationship (Pedersen et al, 2001;Saxena and Ananthasuresh, 2001); one can also design CMs to follow linear or nonlinear paths (Pedersen et al, 2001;Saxena, 2005). This is very essential since designers can directly, precisely and quantitatively control the inputs and outputs; while F1-F14 are only for the qualitative design CMs.…”

“…In the literature, flexibility, stiffness, mechanical efficiency (ME), mechanical advantage (MA), geometrical advantage (GA), weight, strength and so on, have been defined as objective functions or constraints (Howell, 2001;Saxena and Ananthasuresh, 2001;Deepak et al, 2009). Ananthasuresh (1994) pioneered the TO of CM design with a multi-criteria model and a spring model.…”

Towards generating diverse topologies of path tracing compliant mechanisms using a local search based multi-objective genetic algorithm procedure

“…Study shows a significant gain in output performance of compliant mechanisms using non-linear analysis compared to linear analysis and the problem is solved using the Method of Moving Asymptotes. In the another study, the geometrically non-linear finite element analysis with frame elements is solved using the sequential quadratic programming (SQP) technique to satisfy prescribed force-deflection specification by output point of the compliant mechanisms [22].…”