This paper deals with the spatial generalizations of two classical planar synthesis problems: the point-angle and the path generation problems. The two planar synthesis problems involve the guidance of a point through specified positions by using planar four-bar linkages. In spatial generalizations, we are concerned with the guidance of an infinitely extended line by using spatial 4C linkages. The equivalent screw triangle is used to derive the synthesis equations of the spatial 4C linkage. By constraining the translational motion in the driving C joint, the RCCC linkage is synthesized. Our results show that the synthesis of the 4C linkage for line guidance yields the same maximum number of positions as the planar four-bar linkage for point guidance. The maximum number of positions of the path generation of a line is nine, while that of the line-angle problem is five. In addition to presenting the spatial generalizations of planar synthesis problems, the results in this paper can be used to design spatial four-bar linkages to match line specifications, in which only a line element, such as a laser beam, is of interest.

References

References
1.
Roth
,
B.
, and
Freudenstein
,
F.
, 1963, “
Synthesis of Path-Generating Mechanisms by Numerical Methods
,”
ASME J. Eng. Ind.
,
85
(
3
), pp.
298
306
.
2.
Tsai
,
L. W.
, and
Lu
,
J. J.
, 1990, “
Coupler-Point Curve Synthesis Using Homotopy Methods
,”
ASME J. Mech. Des.
,
112
(
3
), pp.
384
389
.
3.
Wampler
,
C. W.
,
Morgan
,
A. P.
, and
Sommese
,
A. J.
, 1992, “
Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages
,”
ASME J. Mech. Des.
,
114
(
1
), pp.
153
159
.
4.
Suh
,
C. H.
, and
Radcliffe
,
C. W.
, 1978,
Kinematics and Mechanism Design
,
John Wiley & Sons
,
New York
.
5.
Roth
,
B.
, 1967, “
On the Screw Axes and Other Special Lines Associated With Spatial Displacements of a Rigid Body
,”
ASME J. Eng. Ind.
,
89B
, pp.
102
110
.
6.
Nielsen
,
J.
, and
Roth
,
B.
, 1995, “
Elimination Methods for Spatial Synthesis
,”
Computational Kinematics
,
J. P.
Merlet
, and
B.
Ravani
, eds.,
Kluwer Academic Publishers
, Dordrecht, pp.
51
62
.
7.
Huang
,
C.
, and
Chang
,
Y. J.
, 2000, “
Polynomial Solution to the Five-Position Synthesis of Spatial CC Dyads via Dialytic Elimination
,”
Proceedings of ASME 2000 Design Engineering Technical Conference
,
Baltimore, MD
, Sept.
10
13
.
8.
McCarthy
,
J. M.
, 1995, “
The Synthesis of Planar RR and Spatial CC Chains and the Equation of a Triangle
,”
ASME J. Mech. Des., Special 50th Anniversary Design Issue
,
117
, pp.
101
106
.
9.
Garcia-Rios
,
I.
,
Palacios-Montufar
,
C.
,
Flores-Campos
J. A.
, and
Osorio-Saucedo
,
R.
, 2009, “
Synthesis of 4C Mechanism for Generation of a Dual Mathematic Function
,”
Appl. Mech. Mater.
,
15
, pp.
67
72
.
10.
Dhall
,
S.
, and
Kramer
,
S. N.
, 1990, “
Design and Analysis of the HCCC, RCCC, and PCCC Spatial Mechanisms for Function Generation
,”
ASME J. Mech. Des.
,
112
, pp.
74
78
.
11.
Larochelle
,
P.
, 1998, “
Spades: Software for Synthesizing Spatial 4C Mechanisms
,”
Proceedings of the 1998 ASME Design Engineering Technical Conferences
,
Atlanta, GA
, Sept.
13
16
.
12.
McCarthy
,
J. M.
, 2000,
Geometric Design of Linkages
,
Springer-Verlag
,
New York
.
13.
Huang
,
C.
, and
Huang
,
B.
, 2009, “
Spatial Generalization of the Planar Path Generation Problem
,”
Computational Kinematics
,
A.
Kecskemethy
, and
A.
Muller
, eds.,
Springer-Verlag
,
Berlin
, pp.
117
124
.
14.
Larochelle
,
P.
, and
Agius
,
A.
, 2005, “
Interactive Visualization of the Coupler Surfaces of the Spatial 4C Mechanism
,”
ASME J. Mech. Des.
,
127
(
6
), pp.
1122
1128
.
15.
Marble
,
S. D.
, and
Pennock
,
G. R.
, 2000, “
Algebraic-Geometric Properties of the Coupler Curves of the RCCC Spatial Four-Bar Mechanism
,”
Mech. Mach. Theory
,
35
, pp.
675
693
.
16.
Tsai
,
L. W.
, and
Roth
,
B.
, 1973, “
Incompletely Specified Displacements: Geometry and Spatial Linkage Synthesis
,”
ASME J. Eng. Ind. B
,
95
(
2
), pp.
603
611
.
17.
Bottema
,
O.
, and
Roth
,
B.
, 1979,
Theoretical Kinematics
,
North-Holland Publishing Company
,
Amsterdam
.
18.
Huang
,
C.
, and
Wang
,
J. C.
, 2003, “
The Finite Screw System Associated With the Displacement of a Line
,”
ASME J. Mech. Des.
,
125
, pp.
105
109
.
19.
Tsai
,
L. W.
, and
Roth
,
B.
, 1972, “
Design of Dyads With Helical, Cylindrical, Spherical, Revolute and Prismatic Joints
,”
Mech. Mach. Theory
,
7
, pp.
85
102
.
20.
Tari
,
H.
,
Su
,
H. J.
, and
Li
,
T. Y.
, 2010, “
A Constrained Homotopy Technique for Excluding Unwanted Solutions From Polynomial Equations Arising in Kinematics Problems
,”
Mech. Mach. Theory
,
45
(
6
), pp.
898
910
.
21.
Murray
,
A.
, and
Larochelle
,
P.
, 1998, “
A Classification Scheme for Planar 4R, Spherical 4R, and Spatial RCCC Linkages to Facilitate Computer Animation
,”
Proceedings of the 1998 ASME Design Engineering Technical Conferences
,
Atlanta, GA
, Sept.
13
16
.
You do not currently have access to this content.