Research Papers

Discretely Deformable Surface Based on Mechanical Interpolation: Application to the Design of a Dynamically Reconfigurable Theater Stage

[+] Author and Article Information
Jean-Philippe Jobin

Département de Génie Mécanique, Université Laval, 1065 avenue de la Médecine, Quebec, QC, G1V 0A6, Canadajobin@gmc.ulaval.ca

Clément Gosselin1

Département de Génie Mécanique, Université Laval, 1065 avenue de la Médecine, Quebec, QC, G1V 0A6, Canadagosselin@gmc.ulaval.ca

This video clip—as well as others cited in the upcoming sections of the paper—will help the reader to understand this paper and hence should be consulted when they are mentioned.

For simplicity, in this analysis, the passive step is always the middle one.

For the rest of this paper, only the branch of solution shown in Fig. 2—i.e., the one for which γi,i=1,2 are equal to +1—will be treated because it is the only one that can locally allow a perfect linear interpolation between the three platforms and hence the only useful branch.


Corresponding author.

J. Mechanisms Robotics 1(1), 011005 (Jul 30, 2008) (9 pages) doi:10.1115/1.2961067 History: Received April 04, 2008; Revised June 23, 2008; Published July 30, 2008

This paper presents the development of an active discretely deformable surface that makes use of mechanical interpolation in order to limit the number of required actuators. First, a planar interpolation mechanism is proposed and optimized in order to minimize the interpolation errors. Then a four-DOF spatial interpolation mechanism with the actuators in the corners is designed based on the planar mechanism. The kinematics of this mechanism are also derived. Finally, a prototype—built in order to illustrate the concept—is presented. The prototype consists of a small-scale dynamically reconfigurable stage for puppet theater performance, referred to as a Castelet. The prototype was used for the creation of two shows that clearly demonstrate the potential of the Castelet in theater performance as well as in other applications.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Simple rectangular flat surface using six autonomous modules comprising 3×3 platforms each

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Figure 2

(a) Schematic representation and (b) parametric descriptions of the planar interpolation mechanism

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Figure 3

The four real solutions for the direct kinematics of the PIM

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Figure 4

The four solutions for the inverse kinematics of the planar interpolation mechanism

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Figure 5

Averaging error Δ as a function of θ for a given set of design parameters

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Figure 6

Schematic (a) top and (b) isometric representations of the four DOF spatial interpolation mechanism

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Figure 7

Schematic (a) top and (b) isometric representations of the constraints automatically imposed to a passive platform

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Figure 8

Notation used to identify the platforms of a 3×3 module

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Figure 9

Angles defining the orientation of the module

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Figure 10

Photographs of (a) four DOF and (b) one DOF modules

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Figure 11

Photograph of the Castelet comprising 20 modules




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