On mechanism design optimization for motion generation

Martin, Peter; Russell, Kevin; Sodhi, Raj S.

doi:10.1016/j.mechmachtheory.2006.11.009

Cited by 21 publications

(11 citation statements)

References 18 publications

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“…al. (1) presented a search algorithm to select motion generators with respect to Grashof conditions, transmission angle conditions and linkage perimeter conditions. Shen et.…”

Section: Introductionmentioning

confidence: 99%

Planar Four-Bar Motion and Path Generation with Order and Branching Conditions

Russell

Shen²

2011

JAMDSM

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This work presents an optimization model for planar four-bar motion and path generation. This model includes the four-bar linkage kinematic model by Suh and Radcliffe (13) as an objective function. This kinematic model allows for the direct minimization of the error between the prescribed and achieved coupler parameters while synthesizing the crank and follower links in a closed loop. Both order and branching conditions are included among the constraint equations.

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“…al. (1) presented a search algorithm to select motion generators with respect to Grashof conditions, transmission angle conditions and linkage perimeter conditions. Shen et.…”

Section: Introductionmentioning

confidence: 99%

Planar Four-Bar Motion and Path Generation with Order and Branching Conditions

Russell

Shen²

2011

JAMDSM

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“…Such a state is possible when the four-bar mechanism reaches a 'lock-up' or binding position. When pivots a 1 , b 1 , and b 0 are collinear, the denominator in equation (17) becomes zero (making the equation and subsequent constraint invalid). The mathematical analysis software MathCAD was used to codify and solve the formulated non-linear optimization problem.…”

Section: Discussionmentioning

confidence: 99%

“…Martin et al [17] presented a selection algorithm for planar four-bar motion generators that considers Grashof criteria, transmission angle criteria, and mechanism perimeter conditions. The algorithm input are the fixed and moving pivot loci calculated for a set of prescribed coupler poses.…”

Section: Motion Generator Selection Algorithmmentioning

confidence: 99%

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Four-bar motion generation with elasticity constraints and optimization

Al-Smadi¹,

Russell

Sodhi

2009

Proceedings of the Institution of Mechanical Engineers, Part K:

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In conventional planar four-bar motion generation, all mechanism links are assumed rigid or non-deforming. Although the assumption of link rigidity in kinematic synthesis may be generally appropriate and often practiced, a statically loaded planar four-bar mechanism will undergo a degree of elastic deflection, particularly the crank and follower links. In this work, a nonlinear optimization problem is formulated for planar four-bar motion generation that considers an applied coupler force and corresponding crank static torque, crank transverse deflection, and follower buckling. The output from the non-linear optimization problem -mechanism fixed and moving pivot loci -are input for a search algorithm that down selects a mechanism solution that satisfies transmission angle conditions, Grashof conditions, and a mechanism compactness condition. The final output of the presented method is planar four-bar motion generator that approximates prescribed coupler poses with satisfactory crank deflection and without follower buckling and also satisfies conditions for link rotatability, transmission angle and compactness.

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“…Automated design of planar mechanisms has been attempted by different researchers and [7][8][9] are some among them. One of the first graph grammar formalism of planar mechanisms was given by Freundenstein [10] which was further developed by Kota [11] and Tsai [12].…”

Section: Introductionmentioning

confidence: 99%

A Graph Grammar Based Scheme for Generating and Evaluating Planar Mechanisms

Radhakrishnan

Campbell

2011

Design Computing and Cognition ’10

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The paper focuses on representing and evaluating planar mechanisms designed using graph grammars. Graph grammars have been used to represent planar mechanisms but there are disadvantages in the methods presently available. This is due to the lack of information in understanding the details of a mechanism represented by the graph since the graphs do not include information about the type of joints and components such as revolute links, prismatic blocks, gears and cams. In order to overcome the drawbacks in the existing methods, a novel representation scheme has been developed. In this method, the authors represent a variety of mechanism types by the use of labels and x, y position information in the nodes. A set of sixteen grammar rules that construct different mechanisms from the basic seed is developed, which implicitly represents a tree of candidate solutions. The scheme is tested to determine its capability in capturing the entire set of feasible planar mechanisms of one degree of freedom. In addition to the representation, another important consideration is the need for an accurate and generalized evaluator for kinematic analysis of the mechanism which, given the lack of information, may not be possible with current design automation schemes. The graph grammar based analysis module is implemented in an existing objectoriented grammar framework and the results have found this to be superior to existing commercial packages. Introduction -An OverviewThe process of designing planar mechanisms usually begins with a clear sense of the mechanisms function which may be in the form of path through space [1]. Cognition of this process is complex since there are a number of variables involved. The typical design process involves 664 P. Radhakrishnan and M.I. Campbell choosing a standard mechanism, customizing the mechanism by adding links, determining kinematic properties using analysis tools and then iterating to determine if the mechanism is able to satisfy the user requirements. In the process, the designer also determines the degrees of freedom, F, using Gruebler's criterion [2], which states where n is the number of links, j 1 refers to number of one degree-offreedom joints (like pivots and sliding blocks) and j 2 refers to the number of two degree-of-freedom joints (like a pin-in-a-slot) in the mechanism. Since most mechanisms have only a single-degree-of-freedom (F = 1) and are comprised of links and joints, the equation (shown above) is compelling as it easily describes what is, and what is not a valid solution. Other than fairly simple geometry methods like three-position synthesis and its higher-order variations, there are no specific guidelines for the design of a mechanism -just this single equation. As a result the design process is time consuming and iterative. This paper attempts a systematic approach of designing planar mechanisms that augments the traditional mechanism design process.The steps involved in the research is presented in Figure 1 which begins with the development of a new graph scheme for r...

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On mechanism design optimization for motion generation

Cited by 21 publications

References 18 publications

Planar Four-Bar Motion and Path Generation with Order and Branching Conditions

Planar Four-Bar Motion and Path Generation with Order and Branching Conditions

Four-bar motion generation with elasticity constraints and optimization

A Graph Grammar Based Scheme for Generating and Evaluating Planar Mechanisms

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