Compliance Analysis of a Three-Legged Rigidly-Connected Platform Device

[+] Author and Article Information
Jian S. Dai

Department of Mechanical Engineering, School of Physical Sciences and Engineering, King’s College London, University of London, The Strand, London WC2R 2LS, UKjian.dai@kcl.ac.uk

Xilun Ding

Department of Mechanical Engineering, School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing, People’s Republic of China

J. Mech. Des 128(4), 755-764 (Sep 11, 2005) (10 pages) doi:10.1115/1.2202141 History: Received December 22, 2004; Revised September 11, 2005

The platform based vibratory bowl feeders are essential elements in automatic assembly. Taking the bowl feeder as a typical three-legged rigidly connected compliant platform device, this paper applies von Mises’ compliance matrix to each of the leaf-spring legs, establishes screw systems of the legs and develops the Jacobian of the platform using the adjoint transformation. Based on the force equilibrium between the supporting and external wrenches and the twist deflection, a platform compliance matrix is proposed as a congruence transformation of the legs’ compliance matrices. The matrix is then decomposed into a central compliance matrix and an adjoint transformation, leading to the decomposition of the legs’ parameter effect from the platform assembly influence. The analysis presents the necessary and sufficient condition for the existence of the twist deflection that is equivalent to the characteristics equation of the compliant platform. Further based on the eigencompliances and eigentwist decomposition, the legs’ parameter effect and the platform assembly parameter influence are identified. This reveals the compliance characteristics of this type of devices and the parameters’ effect on the compliance and presents a suitable parameter range for design of the compliant platform device.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

A vibratory bowl feeder

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Figure 2

Geometry of the compliant platform device

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Figure 3

A leaf-spring leg

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Figure 4

The mounting angles of the leaf-spring leg 1 in the platform

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Figure 5

The mounting configuration of the leaf-spring legs in the platform

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Figure 6

The eigencompliances varying with the equivalent thickness of the leaf-spring legs

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Figure 7

A pair of eigencompliances varying with both width and equivalent thickness

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Figure 8

Eigencompliances with respect to the change of link length

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Figure 9

The pair of eigencompliances with respect to the change of θ (rad)

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Figure 10

The pair of eigencompliances with respect to the change of ϕ (rad)

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Figure 11

Eigencompliance pair with respect to the change of both mounting angles θ and ϕ



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