On Synthesis of Contact Aided Compliant Mechanisms Using the Material Mask Overlay Method

2015 ◽  
Author(s):  
Prabhat Kumar ◽  
Roger A. Sauer ◽  
Anupam Saxena
Keyword(s):  
Compliant Mechanisms ◽  
Synthesis Method ◽  
Mean Value ◽  
Contact Analysis ◽  
Element Formulation ◽  
Active Set ◽  
Set Constraints ◽  
Mean Value Coordinates ◽  
Smooth Path ◽  
The Continuum

Contact Aided Compliant Mechanisms (CCMs) are synthesized via the Material Mask Overlay Strategy (MMOS) to trace a desired non-smooth path. MMOS employs hexagonal cells to discretize the design region and engages negative circular masks to designate material states. To synthesize CCMs, the modified MMOS presented herein involves systematic mutation of five mask parameters through a hill climber search to evolve not only the continuum topology (slave surfaces), but also, to introduce the desired rigid, interacting surfaces within some masks. Various geometric singularities are subdued via hexagonal cells though numerous V-notches get retained at the continuum boundaries. To facilitate contact analysis, boundary smoothing is performed by shifting boundary nodes of the evolving continuum systematically. Numerous hexagonal cells get morphed into concave sub-regions as a consequence. Large deformation finite element formulation with Mean Value Coordinates (MVC) based shape functions is used to cater to the generic hexagonal shapes. Contact analysis is accomplished via the Newton-Raphson iterations with load increment in conjunction with the penalty method and active set constraints. An objective function based on Fourier Shape Descriptors is minimized subject to suitable design constraints. An example of a path generating CCM is included to establish the efficacy of the proposed synthesis method.

Synthesis of C0 Path-Generating Contact-Aided Compliant Mechanisms Using the Material Mask Overlay Method

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Prabhat Kumar ◽  
Roger A. Sauer ◽  
Anupam Saxena
Keyword(s):  
Compliant Mechanisms ◽  
Synthesis Method ◽  
Mean Value ◽  
Contact Boundary ◽  
Element Formulation ◽  
Active Set ◽  
Set Constraints ◽  
Mean Value Coordinates ◽  
Augmented Lagrange Multiplier ◽  
The Continuum

Contact-aided compliant mechanisms (CCMs) are synthesized via the material mask overlay strategy (MMOS) to trace desired nonsmooth paths. MMOS employs hexagonal cells to discretize the design region and engages negative circular masks to designate material states. To synthesize CCMs, the modified MMOS presented herein involves systematic mutation of five mask parameters through a hill climber search to evolve not only the continuum topology but also to position the rigid, interacting surfaces within some masks. To facilitate analysis with contact, boundary smoothing is performed by shifting boundary nodes of the evolving continuum. Various geometric singularities are subdued via hexagonal cells, and the V-notches at the continuum boundaries are alleviated. Numerous hexagonal cells get morphed into concave subregions as a consequence. Large deformation finite-element formulation with mean-value coordinates based shape functions is used to cater to the generic hexagonal shapes. Contact analysis is accomplished via the Newton–Raphson (NR) iteration with load incrementing in conjunction with the augmented Lagrange multiplier method and active set constraints. An objective function based on Fourier shape descriptors (FSDs) is minimized subject to suitable design constraints. Two examples of path-generating CCMs are presented, their performance compared with a commercial software and fabricated to establish the efficacy of the proposed synthesis method.

scholarly journals Computational Synthesis of Large Deformation Compliant Mechanisms Undergoing Self and Mutual Contact

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Prabhat Kumar ◽  
Anupam Saxena ◽  
Roger A. Sauer
Keyword(s):  
Large Deformation ◽  
Compliant Mechanisms ◽  
Mean Value ◽  
Active Set ◽  
Mutual Contact ◽  
Mean Value Coordinates ◽  
Computational Synthesis ◽  
Augmented Lagrange Multiplier ◽  
Rigid Contact ◽  
Boundary Smoothing

Topologies of large deformation contact-aided compliant mechanisms (CCMs), with self and mutual contact, exemplified via path generation applications, are designed using the continuum synthesis approach. Design domain is parameterized using honeycomb tessellation. Assignment of material to each cell, and generation of rigid contact surfaces, are accomplished via suitably sizing and positioning negative circular masks using the stochastic hill-climber search. To facilitate contact analysis, boundary smoothing is implemented. Mean value coordinates are employed to compute shape functions, as many regular hexagonal cells get degenerated into irregular, concave polygons as a consequence of boundary smoothing. Both geometric and material nonlinearities are considered. The augmented Lagrange multiplier method with a formulated active set strategy is employed to incorporate both self and mutual contact. Synthesized contact-aided compliant continua trace paths with single, and importantly, multiple kinks and experience multiple contact interactions pertaining to both self and mutual contact modes.

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

1999 ◽  
Vol 123 (1) ◽  
pp. 33-42 ◽  
Author(s):  
A. Saxena ◽  
G. K. Ananthasuresh
Keyword(s):  
Finite Element ◽  
Linear Models ◽  
Compliant Mechanisms ◽  
Synthesis Method ◽  
Design Sensitivity ◽  
Finite Element Models ◽  
Geometrically Nonlinear ◽  
Linear Elastic ◽  
Nonlinear Design ◽  
Nonlinear Force

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.

Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation

1999 ◽  
Vol 123 (4) ◽  
pp. 535-541 ◽  
Author(s):  
L. Saggere ◽  
S. Kota
Keyword(s):  
Compliant Mechanisms ◽  
Shape Change ◽  
Synthesis Method ◽  
Elastic Equilibrium ◽  
Body Motion ◽  
Motion Generation ◽  
Generation Task ◽  
Potential Applications ◽  
Flexible Segment ◽  
Definition Of

Compliant four-bar mechanisms treated in previous works consisted of at least one rigid moving link, and such mechanisms synthesized for motion generation tasks have always comprised a rigid coupler link, bearing with the conventional definition of motion generation for rigid-link mechanisms. This paper introduces a new task called compliant-segment motion generation where the coupler is a flexible segment and requires a prescribed shape change along with a rigid-body motion. The paper presents a systematic procedure for synthesis of single-loop compliant mechanisms with no moving rigid-links for compliant-segment motion generation task. Such compliant mechanisms have potential applications in adaptive structures. The synthesis method presented involves an atypical inverse elastica problem that is not reported in the literature. This inverse problem is solved by extending the loop-closure equation used in the synthesis of rigid-links to the flexible segments, and then combining it with elastic equilibrium equation in an optimization scheme. The method is illustrated by a numerical example.

Mean value coordinates for closed triangular meshes

2005 ◽  
Vol 24 (3) ◽  
pp. 561-566 ◽  
Author(s):  
Tao Ju ◽  
Scott Schaefer ◽  
Joe Warren
Keyword(s):  
Mean Value ◽  
Triangular Meshes ◽  
Mean Value Coordinates

Topology Synthesis of Large-Displacement Compliant Mechanisms

1999 ◽  
Author(s):  
Claus B. W. Pedersen ◽  
Thomas Buhl ◽  
Ole Sigmund
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Problem ◽  
Adjoint Method ◽  
Compliant Mechanisms ◽  
Large Displacement ◽  
Element Formulation ◽  
Method Of Moving Asymptotes ◽  
Synthesis Tool ◽  
Lagrangian Finite Element ◽  
Moving Asymptotes

Abstract This paper describes the use of topology optimization as a synthesis tool for the design of large-displacement compliant mechanisms. An objective function for the synthesis of large-displacement mechanisms is proposed together with a formulation for synthesis of path-generating compliant mechanisms. The responses of the compliant mechanisms are modelled using a Total Lagrangian finite element formulation, the sensitivity analysis is performed using the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. Procedures to circumvent some numerical problems are discussed.

On Optimization of 2D Compliant Mechanisms Using Honeycomb Discretization With Material-Mask Overlay Strategy

2007 ◽  
Author(s):  
Anupam Saxena
Keyword(s):  
Genetic Algorithm ◽  
Compliant Mechanisms ◽  
Optimal Solutions ◽  
Free Rotation ◽  
Post Processing ◽  
Hexagonal Cell ◽  
Rectangular Cell ◽  
New Material ◽  
Assignment Approach ◽  
The Continuum

Novel honeycomb tessellation and material mask overlay methods are proposed in this paper to obtain optimal planar compliant topologies free from checkerboard and point flexure pathologies. A cardinal reason, namely the presence of strain-free rotation regions in rectangular cell based discretization is identified to be a cause in appearance of such singularities. With each hexagonal cell sharing an edge with its neighboring cells, strain-free displacements are not permitted anywhere in the continuum. The new material assignment approach manipulates material within a group of cells as opposed to a single cell thereby reducing the number of variables making optimization efficient. Optimal solutions obtained are free from intermediate material states and can be manufactured directly after design, without requiring any post processing. The proposed procedure is illustrated using two classical examples in 2D compliant mechanisms solved using genetic algorithm.

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