The plane joint, often referred to as the “E” joint is modeled using dual-number coordinate-transformation matrices. The joint consists of two flat surfaces held in contact so that three degrees of freedom are allowed, two translations and a rotation. The swash-plate mechanism is used as an example of a mechanism featuring the plane joint.

Issue Section:
Research Papers
Topics:
Degrees of freedom, Modeling, Rotation
1.
Cooney, Jr., Charles, E., and Wagner, Elmer R. Universal Joint and Driveshaft Design Manual Society of Automotive Engineers, 1979, pp. 127–130.
2.
Craig, John J., Introduction to Robotics, Mechanics and Controls Addison-Wesley Publishing Co., 1986, ISBN 0-201-10326-5.
3.
Edge
K. A.
, and
Darling
J.
, “
The Pumping Dynamics of Swash Plate Piston Pumps
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT AND CONTROL
June
1989
, Vol.
111
, pp.
307
–
312
.
4.
Engineering March 11, 1921, Vol. 6, “The Michell Crankless Steam Engine,” pp. 290–291.
5.
Fischer, Ian S., Dual-Number Methods in Kinematics, Statics and Dynamics CRC Press, Boca Raton, FL, 1999, ISBN 0-8493-9115-6, Eqs. 189, 192.
6.
Freudenstein
F.
, and
Maki
E. R.
, “
Kinematic Structure of Mechanisms for Fixed and Variable-Stroke Axial-Piston Reciprocating Engines
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS AND AUTOMATION IN DESIGN
September
1984
Vol.
106
, pp.
355
–
364
.
7.
Galin
R.
, and
Harris
C. O.
, “
A Typical Problem in Engineering: Balance a Swashplate Mechanism Used in an Automotive Air Conditioning System Compressor
,”
General Motors Engineering Journal
fourth-quarter
1963
Vol.
10
, pp.
19
–
49
.
8.
Galin
R.
, and
Harris
C. O.
, “
Solution to the Previous Problem: Balance a Swashplate Mechanism Used in an Automotive Air Conditioning System Compressor
,”
General Motors Engineering Journal
first-quarter
1964
Vol.
4
, pp.
53
–
56
.
9.
Iinoue
Kiyoshi
and
Masakasu
Nakasato
, “
Study of the Operating Moment of a Swash Plate Type Axial Piston Pump First Report
,”
Journal of Fluid Control
,
1994
, Vol.
22
, pp.
7
–
29
.
10.
Maki
E. R.
, and
DeHart
A. O.
, “
A New Look at Swash-Plate Drive Mechanisms
,”
SAE Transactions
,
1971
, Vol.
80
, pp.
2712
–
2722
.
11.
Michell, Anthony G. M., “Crankless Reciprocating Machines,” ASME Transactions, May–August, 1930, pp. 85–89.
12.
Paul, Richard P., Robot Manipulators, Mathematics, Programming and Control, MIT Press, 1918, ISBN 0-262-16082.
13.
Sandor, George N., and Erdman, Arthur G., Advanced Mechanism Design: Analysis and Synthesis, Vol. 2, 1984, Prentice-Hall, ISBN 0-13-011437-5.
14.
Weibel
J.
, and
Mantey
R.
, “
The Engineering Development of a Compressor for Automotive Air Conditioning Systems
,”
General Motors Engineering Journal
fourth-quarter,
1963
, Vol.
10
, pp.
19
–
24
.
15.
Yang
A. T.
, “
Displacement Analysis of Spatial Five-Link Mechanisms Using (3 × 3) Matrices With Dual-Number Elements
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, February
1969
, Vol.
91
, pp.
152
–
157
.
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