Some engineering applications require structures to expand and contract in size, while retaining their exterior shape. The applications range from mundane daily life objects to more fancy art structures. In contrast to a multi degree-of-freedom structure, a single degree-of-freedom structure can be driven by a single actuator, reducing cost and simplifying the control. In this paper, we study single degree-of-freedom structures that can be formed by a lattice of single degree-of-freedom polyhedral expanding units. Due to built-in symmetries, the entire structure can expand and contract as one of the units in the structure is actuated. The paper describes the design of polyhedral single degree-of-freedom systems, the structures of their dynamics/optimal control, and results from construction prototypes.

1.
Hoberman, C., 2000, “Expandagon,” website: www.hoberman.com,.
2.
Wolhart, K., 1995, “New Overconstrained Spheroidal Linkages,” World Congress on the Theory of Machines and Mechanisms, Milano, Vol. 1, pp. 149–154.
3.
Pfister
,
F.
, and
Agrawal
,
S. K.
,
1999
, “
Analytical Dynamics of Unrooted Multibody Systems with Symmetries
,”
ASME J. Mech. Des.
,
121
(
3
), pp.
440
447
.
4.
Rus, D., and Vona, M., 1999, “Self-reconfiguration Planning with Compressible Unit Modules,” 1999 IEEE International Conference on Robotics & Automation, May.
5.
Yim, M., Duff, D. G., and Roufas, K. D., 2000, “Polybot: A Modular Reconfigurable Robot,” IEEE International Conference on Robotics and Automation, Vol. 1.
6.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press.
7.
Artobolevsky, I. I., 1976, Mechanisms in Modern Engineering Design, Volumes I-V, Mir Publishers, Moscow.
8.
Erdman, A. G., 1993, Modern Kinematics: Development in the Last 40 Years, Wiley Series in Design Engineering.
9.
Fuller, R. Buckminster, Applewhite, E. J., and Loeb, A. L., 1975, Synergistics, Macmillan, New York.
10.
Pugh, A., 1976, Polyhedra A Visual Approach, University of California Press, Berkeley and Los Angeles, California.
11.
Athans, M., and Falb, P. L., 1966, Optimal Control: An Introduction to the Theory and Applications, McGraw Hill, New York.
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