The components of force and torque acting on a joint of a link in static equilibrium are partitioned according to the type of joint so that the equations of static equilibrium can be set up automatically by computer where the type of each joint has been specified in the input data. Special attention is given to the cylindrical joint, and the implications of the geometry of an intermediate link with a cylindrical joint on both ends are examined. While the methodology is demonstrated for the RCCC mechanism, which features a revolute input joint and cylindrical intermediate and output joints, it is adaptable to closed-loop mechanisms of binary links with any kind of joint in any position.

1.
Yang
,
A. T.
, and
Freudenstein
,
F.
, 1964, “
Application of Dual-Number Quaternion Algebra to the Analysis of Spatial Mechanisms
,”
ASME J. Appl. Mech.
0021-8936,
86
, pp.
300
308
.
2.
Fischer
,
I. S.
, 1999,
Dual-Number Methods in Kinematics, Statics and Dynamics
CRC
,
Boca Raton, FL
.
3.
Yang
,
A. T.
, 1965, “
Static Force and Torque Analysis of Spherical Four-Bar Mechanisms
,”
ASME J. Eng. Ind.
0022-0817,
87
, pp.
221
227
.
4.
Bagci
,
C.
, 1971, “
Static Force and Torque Analysis Using 3×3 Screw Matrix, and Transmission Criteria for Space Mechanisms
,”
ASME J. Eng. Ind.
0022-0817,
94
, pp.
783
745
.
5.
Keler
,
M. L.
, 1973, “
Kinematics and Statics Including Friction in Single-Loop Mechanisms by Screw Calculus and Dual Vectors
,”
ASME J. Eng. Ind.
0022-0817,
95
, pp.
471
480
.
6.
Fischer
,
I. S.
, and
Freudenstein
,
F.
, 1984, “
Internal Force and Moment Transmission in a Cardan Joint With Manufacturing Tolerances
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
106
, pp.
301
311
.
7.
Larochelle
,
P.
, and
McCarthy
,
J. M.
, 1992, “
Static Analysis of Spherical nR Kinematic Chains with Joint Friction
,”
Proceedings of the ASME Mechanisms Conference
,
Scotsdale, AZ
,
DE-47
, pp.
173
177
.
8.
Watanabe
,
K.
,
Kawakatsu
,
T.
, and
Nakao
,
S.
, 2005, “
Kinematic and Static Analyses of Tripod Constant Velocity Joints of the Spherical End Spider Type
,”
ASME J. Mech. Des.
1050-0472,
127
, pp.
1137
1144
.
9.
Shai
,
O.
, and
Pennock
,
G. R.
, 2006, “
Extension of Graph Theory to the Duality Between Static Systems and Mechanisms
,”
ASME J. Mech. Des.
1050-0472,
128
, pp.
179
191
.
10.
Sui
,
H.-J.
, and
McCarthy
,
J. M.
, 2006, “
A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms
,”
ASME J. Mech. Des.
1050-0472,
128
, pp.
776
786
.
11.
Perkins
,
D. A.
,
Turner
,
M. L.
, and
Murray
,
A. P.
, 2007, “
Static Analysis of Torque and Coupler Driven Spherical Four-Bar Mechanisms With an Applied Load
,”
ASME Proceedings of the ASME Mechanisms Conference
,
Las Vegas NV
.
12.
Craig
,
J. J.
, 1986,
Introduction to Robotics, Mechanics and Control
,
Addison-Wesley
,
Reading, MA
.
13.
Davidson
,
J. K.
, and
Hunt
,
K. H.
, 2004,
Robots and Screw Theory, Applications of Kinematics and Statics to Robotics
,
Oxford University Press
,
New York
.
14.
Duffy
,
J.
, 1996,
Robotics and Kinematics with Applications to Robotics
,
Cambridge University Press
,
Cambridge
.
15.
Paul
,
R. R.
, 1981,
Robot Manipulators, Mathematics, Programming, and Control
,
MIT
,
Cambridge, MA
.
16.
Nikravesh
,
P. E.
, 1988,
Computer-Aided Analysis of Mechanical Systems
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
17.
Haug
,
E. J.
, 1992,
Intermediate Dynamics
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
18.
Yang
,
A. T.
, 1963, “
Application of Quaternion Algebra and Dual numbers to the Analysis of Spatial Mechanism
,” thesis, Columbia University.
19.
Liu
,
T.
, and
Lee
,
T. W.
, 1984 “
Kinematic Structural Analysis of Overconstrained Spatial Mechanisms, Part I: Theory
,” ASME Paper No. 84-DET-215.
You do not currently have access to this content.