Two problems are addressed in this paper. First, the mathematical model to perform the static analysis of an antiprism tensegrity structure subjected to a wide variety of external loads is presented. The virtual work approach is used to deduce the equilibrium equations and a method based on Newton’s Third Law is used to verify the numerical results. Two numerical examples are provided to demonstrate the use of the mathematical model, as well as the verification method. The second problem deals with the development of a mathematical model to perform the static analysis of a prestressed antiprism tensegrity structure subjected to an arbitrary length reduction of its connecting ties. Again, a virtual work approach is used to deduce the equilibrium equations and the numerical results are verified using a Newtonian approach. One example is provided to illustrate the mathematical model.

Keywords:
structural engineering computing, stress analysis
Topics:
Equilibrium (Physics), Struts (Engineering), Tensegrity structures
1.
Yin
,
J. P.
,
Duffy
,
J.
, and
Crane
,
C.
,
2002
, “
An Analysis for the Design of Self-Deployable Tensegrity and Reinforced Tensegrity Prisms with Elastic Ties
,”
Int. J. Robotics Automation, Special Issue on Compliance and Compliant Mechanisms
,
17
,
Issue 1
Issue 1
.
2.
Tobie, R. S., 1976, “A Report on an Inquiry into the Existence, Formation and Representation of Tensile Structures,” Master of Industrial Design thesis, Pratt Institute, NY.
3.
Kenner, H., 1976, Geodesic Math and How to Use It, University of California Press, Berkeley, CA.
4.
Stern, I. P., 1999, “Development of Design Equations for Self-Deployable N-Strut Tensegrity Systems,” Master of Science thesis, University of Florida, Gainesville, FL.
5.
Knight, B. F., 2000, “Deployable Antenna Kinematics using Tensegrity Structure Design,” Ph.D. thesis, University of Florida, Gainesville, FL.
6.
Crane, C., and Duffy, J., 1998, Kinematic Analysis of Robot Manipulators, Cambridge University Press, New York.
7.
Doughty, S., 1998, Mechanics of Machines, Wiley, New York.
8.
Kunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford University Press, New York.
9.
Lee
,
J.
,
Duffy
,
J.
, and
Hunt
,
K.
,
1998
, “
A Practical Quality Index Based on the Octahedral Manipulator
,”
Int. J. Robotics Res.
,
17
, pp.
1081
–
1090
.
10.
Hines, R., 1995, “Catastrophe Analysis of Compliant Mechanisms,” Master’s of Science thesis, University of Florida, Gainesville, FL.
11.
Arnold’s, V. I., 1992, Catastrophe Theory, Springer, Berlin.
Copyright © 2005
 by ASME
You do not currently have access to this content.