This paper addresses the kinematic analysis of a three-degree of freedom (DOF) compliant platform able to move in three dimensional space. The device is formed by the actuators, a central moving platform, and compliant joints. The actuators are three binary links. The moving platform is an equilateral plate. Springs connect the free end of each actuator with each vertex of the central platform. In this way, the motion of the actuators is transmitted to the moving platform. Compliant joints increase the complexity of the motion of the central platform and few studies have been carried out. This paper focuses on the forward and reverse analyses for the platform and the derivation of equations that relate the velocity of the moving platform with the velocity of the actuators.

References

References
1.
Fuller
,
R.
,
1975
,
Synergetics, Explorations in the Geometry of Thinking
,
Collier Macmillan
,
London
.
2.
Kenner
,
H.
,
1976
,
Geodesic Math and How to Use It
,
University of California Press
,
Berkeley, CA
.
3.
Calladine
,
C.
,
1978
, “
Buckminster Fuller's Tensegrity Structures and Clerk Maxwell's Rules for the Construction of Stiff Frames
,”
Int. J. Solids Struct.
,
14
, pp.
161
172
.10.1016/0020-7683(78)90052-5
4.
Murakami
,
H.
,
2001
, “
Static and Dynamic Analyses of Tensegrity Structures. Part 1. Nonlinear Equations of Motion
,”
Int. J. Solids Struct.
,
38
, pp.
3599
3613
.10.1016/S0020-7683(00)00232-8
5.
Crane
,
C.
,
Duffy
,
J.
, and
Correa
,
J.
,
2005
, “
Static Analysis of Tensegrity Structures
,”
ASME J. Mech. Des.
,
127
(
2
), pp.
257
268
.10.1115/1.1804194
6.
Knight
,
B. F.
,
2000
, “
Deployable Antenna Kinematics Using Tensegrity Structure Design
,” Ph.D. thesis, University of Florida, Gainesville, FL.
7.
Sultan
,
C.
, and
Corless
,
M.
,
2000
, “
Tensegrity Flight Simulator
,”
J. Guid. Control Dyn.
,
23
(
6
), pp.
1055
1064
.10.2514/2.4647
8.
Tibert
,
A.
, and
Pellegrino
,
S.
,
2002
, “
Deployable Tensegrity Reflectors for Small Satellites
,”
J. Spacecr. Rockets
,
39
(
5
), pp.
701
709
.10.2514/2.3867
9.
Sultan
,
C.
, and
Skelton
,
R.
,
2004
, “
A Force and Torque Tensegrity Sensor
,”
Sens. Actuators A
,
112
(
2–3
), pp.
220
231
.10.1016/j.sna.2004.01.039
10.
Ingber
,
D.
,
2003
, “
Tensegrity I. Cell Structure and Hierarchical Systems Biology
,”
J. Cell. Sci.
,
116
, pp.
1157
1173
.10.1242/jcs.00359
11.
Fest
,
E.
,
Shea
,
K.
,
Domer
,
B.
, and
Smith
,
F. C.
,
2003
, “
Adjustable Tensegrity Structures
,”
J. Struct. Eng.
,
129
(
4
), pp.
515
526
.10.1061/(ASCE)0733-9445(2003)129:4(515)
12.
Sultan
,
C.
, and
Skelton
,
R.
,
2003
, “
Deployment of Tensegrity Structures
,”
Int. J. Solids Struct.
,
40
, pp.
4637
4657
.10.1016/S0020-7683(03)00267-1
13.
Arsenault
,
M.
, and
Gosselin
,
C. M.
,
2006
, “
Kinematic, Static and Dynamic Analysis of a Planar 2-DOF Tensegrity Mechanism
,”
Mech. Mach. Theory
,
41
, pp.
1072
1089
.10.1016/j.mechmachtheory.2005.10.014
14.
Arsenault
,
M.
,
2011
, “
Stiffness Analysis of a 2DOF Planar Tensegrity Mechanism
,”
J. Mech. Rob.
,
3
(
2
), p.
021011
.10.1115/1.4003849
15.
Hernandez
,
S.
, and
Mirats
,
J.
,
2008
, “
Tensegrity Frameworks: Static Analysis Review
,”
Mech. Mach. Theory
,
43
, pp.
859
881
.10.1016/j.mechmachtheory.2007.05.006
16.
McCarthy
,
J. M.
,
2011
, “
21st Century Kinematics: Synthesis, Compliance, and Tensegrity
,”
J. Mech. Rob.
,
3
(
2
), p.
020201
.10.1115/1.4003181
17.
Pelesko
,
J.
, and
Bernstein
,
D.
,
2002
,
Modeling MEMS and NEMS
,
CRC Press
,
Boca Raton, FL
.
18.
Ebefors
,
T.
,
Mattsson
,
J.
,
Kalvesten
,
E.
, and
Stemme
,
G.
,
1999
, “
A Robust Micro Conveyer Realized by Arrayed Polymide Joint Actuators
,”
Proceedings of the 12th IEEE Conference on Micro Electro Mechanical Systems
,
Orlando, FL
, pp.
576
581
.
19.
Suh
,
J.
,
Darling
,
R.
,
Bohringer
,
K.
,
Donald
,
B.
,
Baltes
,
H.
, and
Kovacs
,
G.
,
1999
, “
CMOS Integrated Ciliary Actuator Array as a General-Purpose Micromanipulation Tool for Small Objects
,”
J. Microelectromech. Syst.
,
8
(
4
), pp.
483
496
.10.1109/84.809064
20.
Chen
,
S.
, and
Culpepper
,
M. L.
,
2006
, “
Design of a Six-Axis Micro-Scale Nanopositioner-uHexFlex
,”
Precis. Eng.
,
30
, pp.
314
324
.10.1016/j.precisioneng.2005.11.002
21.
Brower
,
D. M.
,
De Jong
,
B. R.
, and
Soemers
,
H. M. J. R.
,
2010
, “
Design and Modeling of a Six DOFs MEMS-Based Precision Manipulator
,”
Precis. Eng.
,
34
, pp.
307
319
.10.1016/j.precisioneng.2009.08.001
22.
Bamberger
,
H.
, and
Shoham
,
M.
,
2007
, “
A Novel Six Degrees-of-Freedom Parallel Robot for MEMS Fabrication
,”
IEEE Trans. Rob.
,
23
(
2
), pp.
189
195
.10.1109/TRO.2006.889493
23.
Liang
,
Q.
, and
Zhang
,
D.
,
2010
, “
Micromanipulator With Integrated Force Sensor Based on Compliant Parallel Mechanism
,”
Proceedings of the 2010 IEEE International Conference on Robotics and Biomimetics
,
Tianjin, China
, pp.
709
714
.
24.
Brand
,
L.
,
1947
,
Vector and Tensor Analysis
,
Wiley
,
New York
.
25.
Duffy
,
J.
,
1996
,
Statics and Kinematics With Applications to Robotics
,
Cambridge University
,
New York
.
26.
Crane
,
C.
, and
Duffy
,
J.
,
1998
,
Kinematic Analysis of Robot Manipulators
,
Cambridge University
,
New York
.
27.
Crane
,
C.
,
Rico
,
J.
, and
Duffy
,
J.
,
2007
,
Screw Theory and its Application to Spatial Robot Manipulators
,
University of Florida
,
Gainesville, FL
.
28.
Tsai
,
L.
,
1999
,
Robot Analysis
,
Wiley
,
New York
.
You do not currently have access to this content.