Checkers Directory Reference

Detailed Description

[Introduction][Geometry][Formulations][Statistics][References]

Introduction

This series of linkages belongs to the family of hinged tesselations. It illustrates the solver on simulating large deployable mechanisms. The tesselation shown above deploys with a one degree of freedom self-motion, and can actually be folded to occupy a single square.

Geometry

Each linkage consists of n x n (with n uneven) square bodies hinged together at their corners by means of revolute joints to form a regular checkers pattern.

Formulations

This directory includes the following Checkers mechanisms:

• Checker3 A deployable checker with 3 squares.
• Checker5 A deployable checker with 5 squares.
• Checker7 A deployable checker with 7 squares.
• Checker9 A deployable checker with 9 squares.

Check each file for detailed instructions about how to solve them.

Statistics

Characteristics of the problems:

	3x3	5x5	7x7	9x9
Nr. of loops	4	16	36	64
Nr. of links	9	25	49	81
Nr. of joints	12	40	84	144
Nr. of equations (in the simplified system)	16	56	120	208
Nr. of variables (in the simplified system)	16	48	72	160

Here you have the statistics about the execution (on an Intel Core i7 at 2.9 Ghz).

	3x3	5x5	7x7	9x9
Nr. of empty boxes	0	0	0	0
Nr. of solution boxes	802	798	801	789
Solver time (s)	11	65	240	721

References

• D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, London, Penguin, pp. 101-103, 1991.

Files
file	Checker3.world [code]
	A 3x3 deployable checker.
file	Checker5.world [code]
	A 5x5 deployable checker.
file	Checker7.world [code]
	A 7x7 deployable checker.
file	Checker9.world [code]
	A 9x9 deployable checker.