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Research Papers

Design Strategies for the Topology Synthesis of Dual Input-Single Output Compliant Mechanisms

[+] Author and Article Information
Charles Kim

Department of Mechanical Engineering, Bucknell University, Lewisburg, PA 17837charles.kim@bucknell.edu

Note that we have selected $lθ=10 mm$ as the normalizing length. This selection only affects the specific value of $ψc$ but does not influence the selection of building blocks to obtain desired kinematic behavior. The value $lθ=10 mm$ will be used throughout this example.

J. Mechanisms Robotics 1(4), 041002 (Sep 02, 2009) (10 pages) doi:10.1115/1.3204252 History: Received July 15, 2008; Revised June 11, 2009; Published September 02, 2009

Abstract

In this paper, design strategies are presented for the topology synthesis of dual input-single output compliant mechanisms. Decomposition methods are proposed to yield tractable subproblems to achieve motion requirements. The methods make use of the single point synthesis, which effectively generates topologies satisfying the motion requirements at one point by assembling compliant building blocks. In this paper, the compliant deviation angle is proposed to measure the ability of building blocks to transmit load with minimal storage of strain energy. The design strategies are versatile in allowing the designer to incorporate auxiliary design considerations and to synthesize mechanism that traverse a locus of output displacements. The building block approach pursued in this paper provides crucial insight to augment designer understanding and ability.

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Figures

Figure 1

Geometric characteristics of the (a) compliance and (b) stiffness ellipsoids

Figure 2

Example results from the (a) single point synthesis and (b) the synthesis method for single input-single output mechanisms; image regenerated from Ref. 16

Figure 3

(a) The original DISO problem statement may be decomposed into (b) two sets of boundary conditions BC1 and BC2 that correspond to two distinct SISO problems

Figure 4

The SISO subproblems BC1 and BC2 are each decomposed into three SPS problems. The resulting subproblems may be addressed by the SPS.

Figure 5

The angle γs−γc represents the difference in primary motion and load-bearing directions of a building block. The building block should be aligned such that the PCVt∥uouti and PSVf∥uoutj. Note that this is a compliant dyad building block, which is parameterized by the lengths of the two beams (l1,l2) and the angle α between them.

Figure 6

(a) n2 and (b) n3 for the compliant dyad shown in Fig. 5(l1=60 mm,  lθ=10 mm)

Figure 7

γs−γc for the compliant dyad shown in Fig. 5(l1=60 mm, lθ=10 mm). Values for 90 deg<α<270 deg have been filtered out because these geometries are not suitable for load-bearing.

Figure 8

Interior submechanisms for generic DISO compliant mechanisms

Figure 9

The locus of attainable output displacements is the parallelogram spanned by Uout1 and Uout2

Figure 10

Flowchart of the steps involved in the synthesis of DISO compliant mechanisms

Figure 11

(a) DISO gripper problem specifications; (b) synthesized output constraints meet the range of desired ψc and provide effective force transmission with the γs−γc values

Figure 12

Output displacement as a function of translation angle and rotation at P2

Figure 13

(a) The beam (dashed line) constrains P2 to translate along uP2. The beam (dash-dot line) transmits displacement at in1 to P2; (b) ANSYS simulation with uin1 actuated

Figure 14

Rapid prototype of DISO gripper shown with (a) uin1 and (b) uin2 applied. An outline of the nondeformed gripper is overlaid on the images to emphasize mechanism deformation and the output displacement.

Figure 15

(a) The specifications dictate that the end of the insect leg must traverse an elliptical path. (b) The elliptical path is enveloped by the locus of displacements. (c) The interior submechanisms are synthesized to provide the displacements Uout1 and Uout2.

Figure 16

(a) Plot of the geometric advantage versus the angle of input translation. (b) Input constraints are synthesized to provide maximum geometric advantage. (c) ANSYS simulation shows nonlinear deformation following along an elliptical path.

Figure 17

A scaled-up proof-of-concept prototype is shown in various positions along the desired elliptical path

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