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TECHNICAL PAPERS

# Force Analysis of a Vibratory Bowl Feeder for Automatic Assembly

[+] Author and Article Information
Richard Silversides

Department of Mechanical Engineering, School of Physical Sciences and Engineering, King’s College London, Strand, London, WC2R 2LS, UKrichard.silversides@kcl.ac.uk

Jian S Dai1

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

Lakmal Seneviratne

Department of Mechanical Engineering, School of Physical Sciences and Engineering, King’s College London, Strand, London, WC2R 2LS, UKlakmal.seneviratne@kcl.ac.uk

Or variously solid damping, internal damping, and natural damping.

1

Corresponding author.

J. Mech. Des 127(4), 637-645 (Aug 27, 2004) (9 pages) doi:10.1115/1.1897407 History: Received February 10, 2004; Revised August 27, 2004

## Abstract

This paper investigates the vibratory bowl feeder for automatic assembly, presents a geometric model of the feeder, and develops force analysis, leading to dynamical modeling of the vibratory feeder. Based on the leaf-spring modeling of the three legs of the symmetrically arranged bowl of the feeder, and equating the vibratory feeder to a three-legged parallel mechanism, the paper reveals the geometric property of the feeder. The effects of the leaf-spring legs are transformed to forces and moments acting on the base and bowl of the feeder. Resultant forces are obtained based upon the coordinate transformation, and the moment analysis is produced based upon the orthogonality of the orientation matrix. This reveals the characteristics of the feeder, that the resultant force is along the $z$-axis and the resultant moment is about the $z$ direction and further generates the closed-form motion equation. The analysis presents a dynamic model that integrates the angular displacement of the bowl with the displacement of the leaf-spring legs. Both Newtonian and Lagrangian approaches are used to verify the model, and an industrial case-based simulation is used to demonstrate the results.

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## Figures

Figure 4

Rotation of the bowl due to bending of the leaf spring

Figure 5

Free body diagram of the static forces acting on the base

Figure 6

Free body diagram of the static forces acting on the bowl

Figure 7

The end moments of the springs acting on the base and bowl

Figure 8

A force rotated uniformly around the axis of the bowl

Figure 9

Linearized movement of the spring end

Figure 3

The geometric arrangement of the vibratory bowl feeder leaf-spring legs

Figure 2

Bending of the leaf springs

Figure 1

Layout of a vibratory bowl feeder

Figure 10

Illustration of the relation between rkpcosϕtp and rkbcosϕtb

Figure 11

Plot of the state variables against time (sine input starting at t=0)

Figure 12

Plot of the absolute positions of the bowl and base against time (after settling)

## Errata

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