Reconfiguration Mechanism With Interlocking Geometric Constraints From Puzzles
Liping Zhang, Jian S. Dai · 2012
This paper proposes a reconfiguration mechanism modelling for puzzles with its interlocking geometric constraints analysis. Wooden puzzles consisting of interlocking assemebly of notched sticks are often referred to as bar-puzzles, sometime known as the Chinese Puzzles or Chinese Cross. The puzzle with multiple reconfigurable pieces as kinematic links leads to topology arrangements. Although its partition or assembly process can be operated as mechanism motions, there does not appear to be any evidence that the idea of its mechanism property and any configuration analysis originated. To this purpose, this paper set up a static and discrete reconfiguration theory of geometric puzzles for modeling the topology changement as Put Together, Take Apart, Sequential Movement and various others. The partition and assembly process analysis aims to extract the kinematic chains as links and joints. The puzzle unlocking leads to configuration constraints rearrangement problems which accompanying pieces of bars self-grouped as defined reconfiguration links and joints. The mathematical recreation of the mechanism structure stems from its interlocking geometric constraints property. This paper reveals its interlocking property as configuration constraints including many passive constraints and further discloses the mechanism constraints modeling in two different partition methods. The puzzle solutions are first described as reconfigurable topology mechanism and the constrained mobility is analyzed based on an ingenious and distinctive reconfiguration property.