Research Papers: Design of Mechanisms and Robotic Systems

Link-Based Performance Optimization of Spatial Mechanisms

[+] Author and Article Information
Yimesker Yihun

Department of Mechanical Engineering,
Idaho State University,
Pocatello, ID
e-mail: yimeyihu@isu.edu

Ken W. Bosworth

Department of Mechanical Engineering,
Idaho State University,
Pocatello, ID
Department of Mathematics,
Idaho State University,
Pocatello, ID
e-mail: boswkenn@isu.edu

Alba Perez-Gracia

Department of Mechanical Engineering,
Idaho State University,
Pocatello, ID
e-mail: perealba@isu.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 24, 2014; final manuscript received July 14, 2014; published online October 20, 2014. Assoc. Editor: Craig Lusk.

J. Mech. Des 136(12), 122303 (Oct 20, 2014) (11 pages) Paper No: MD-14-1190; doi: 10.1115/1.4028304 History: Received March 24, 2014; Revised July 14, 2014

In the design of spatial linkages, the finite-position kinematics is fully specified by the position of the joint axes, i.e., a set of lines in space. However, most of the tasks have additional requirements regarding motion smoothness, obstacle avoidance, force transmission, or physical dimensions, to name a few. Many of these additional performance requirements are fully or partially independent of the kinematic task and can be fulfilled using a link-based optimization after the set of joint axes has been defined. This work presents a methodology to optimize the links of spatial mechanisms that have been synthesized for a kinematic task, so that additional requirements can be satisfied. It is based on considering the links as anchored to sliding points on the set of joint axes, and making the additional requirements a function of the location of the link relative to the two joints that it connects. The optimization of this function is performed using a hybrid algorithm, including a genetic algorithm (GA) and a gradient-based minimization solver. The combination of the kinematic synthesis together with the link optimization developed here allows the designer to interactively monitor, control, and adjust objectives and constraints, to yield practical solutions to realistic spatial mechanism design problems.

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Grahic Jump Location
Fig. 1

CAD model for manual adjustment and optimization; sliding anchor point from (a) to (b) and from (c) to (d)

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Fig. 2

Overall design strategy. Link-based optimization stages are shown inside the broken lines.

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Fig. 3

Joint axes for two spatial mechanism topologies: (a) a closed linkage, CRR–RRR; (b) a linkage with a tree structure, 3R-(2R,2R)

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Fig. 4

Constraint region represented by a cylindrical surface

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Fig. 5

Constraint region represented by a spherical surface

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Fig. 6

Schematic diagram for the transmission angle

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Fig. 7

Desired trajectory of the CRR–RRR linkage

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Fig. 8

Trajectory for the Bennett linkage

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Fig. 9

Initial CRR-RRR mechanism. Darker lines, corresponding to links, are located at the common normal lines between joints (depicted in a lighter shade).

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Fig. 10

Mechanism obtained after link length constraints used

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Fig. 11

Different configurations of the mechanism obtained after region avoidance constraint is used

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Fig. 12

Mechanism obtained after optimizing region avoidance, overall length and force transmission

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Fig. 13

Motion of the mechanism obtained after optimizing region avoidance, overall length and force transmission. Five positions along the trajectory are reached by the mechanism while avoiding the obstacle (lighter lines corresponding to joint axes, darker lines corresponding to the links, including the end-effector link).

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Fig. 14

The CAD model for the final optimized solution at three different configurations

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Fig. 15

The Bennett linkage used as a hinge and a cabinet door (courtesy of PsiStar Solutions)

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Fig. 16

Initial solution of the Bennett linkage

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Fig. 17

Optimized Bennett linkage with only link length constraints

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Fig. 18

Mechanism with only obstacle avoidance and offset constraint. The blue square corresponds to the cabinet door.

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Fig. 19

Mechanism obtained with link length, offset length, and obstacle avoidance constraints

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Fig. 20

Motion of the final design for the cabinet linkage



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