This paper presents a geometric method as a unified synthesis process of function generation for spatial linkages. The synthesis method utilizes the mapping relationship between spatial kinematic geometric model and two-plane projection system to transform the problem from spatial geometry to plane geometry. In this way, the synthesis process of mechanisms can be simplified through the corresponding transformation. Afterward, the line-guidance model is built up. Combining the kinematic inversion in two-plane projection system, this model can be used to realize the spatial linkages synthesis for function generation with three finite positions. Finally, revolute–sphere–sphere–revolute (RSSR) and revolute–sphere–sphere–prism (RSSP) mechanisms are offered to illustrate the application of this method.

References

References
1.
Sandor
,
G. N.
,
1968
, “
Principles of a General Quaternion-Operator Method of Spatial Kinematic Synthesis
,”
ASME J. Appl. Mech.
,
35
(
1
), pp.
40
46
.
2.
Hartenberg
,
R. S.
, and
Denavit
,
J.
,
1964
,
Kinematic Synthesis of Linkages
,
McGraw-Hill
,
New York
.
3.
Roth
,
B.
,
1967
, “
The Kinematics of Motion Through Finitely Separated Positions
,”
ASME J. Appl. Mech.
,
34
(
3
), pp.
591
598
.
4.
Wang
,
D.
, and
Wang
,
W.
,
2015
,
Kinematic Differential Geometry and Saddle Synthesis of Linkages
,
Wiley
,
Singapore
.
5.
Fischer
,
I.
,
1998
,
Dual-Number Methods in Kinematics, Statics and Dynamics
,
CRC Press
,
Boca Raton, FL
.
6.
Raghavan
,
M.
, and
Roth
,
B.
,
1995
, “
Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators
,”
ASME J. Mech. Des.
,
117
(
B
), pp.
71
79
.
7.
Wampler
,
C. W.
,
Morgan
,
A. P.
, and
Sommese
,
A. J.
,
1990
, “
Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics
,”
ASME J. Mech. Des.
,
112
(
1
), pp.
59
68
.
8.
McGarva
,
J. R.
,
1994
, “
Rapid Search and Selection of Path Generating Mechanisms From a Library
,”
Mech. Mach. Theory
,
29
(
2
), pp.
223
235
.
9.
Li
,
X.
,
Wu
,
J.
, and
Ge
,
Q. J.
,
2016
, “
A Fourier Descriptor-Based Approach to Design Space Decomposition for Planar Motion Approximation
,”
ASME J. Mech. Rob.
,
8
(
6
), pp.
699
708
.
10.
Mullineux
,
G.
,
2011
, “
Atlas of Spherical Four-Bar Mechanisms
,”
Mech. Mach. Theory
,
46
(
11
), pp.
1811
1823
.
11.
Chu
,
J.
, and
Cao
,
W.
,
1992
, “
A New Method of Dimension Analysis and Synthesis about Planar Linkage Function Generators—Frequency Analyzing Method Curves
,”
J. Mech. Sci. Technol.
,
43
(
3
), pp.
7
13
.
12.
Sun
,
J.
,
Wang
,
P.
,
Liu
,
W.
, and
Chu
,
J.
,
2018
, “
Non-Integer-Period Motion Generation of a Planar Four-Bar Mechanism Using Wavelet Series
,”
Mech. Mach. Theory
,
121
, pp.
28
41
.
13.
Sun
,
J.
, and
Chu
,
J.
,
2009
, “
Fourier Method to Function Synthesis of an RCCC Mechanism
,”
Proc. Inst. Mech. Eng., Part C.
,
223
(
2
), pp.
503
513
.
14.
Sun
,
J.
,
Liu
,
W.
, and
Chu
,
J.
,
2015
, “
Dimensional Synthesis of Open Path Generator of Four-Bar Mechanisms Using the Haar Wavelet
,”
ASME J. Mech. Des.
,
137
(
8
), p.
082303
.
15.
Bagci
,
C.
,
1984
, “
Geometric Methods for the Synthesis of Spherical Mechanisms for the Generation of Functions, Paths and Rigid-Body Positions Using Conformal Projections
,”
Mech. Mach. Theory
,
19
(
1
), pp.
113
127
.
16.
Jiang
,
D.
,
1990
, “
Stereographic Projection Method for Synthesis of Spherical Four-Bar Mechanisms
,”
J. Northwestern Polytechnical Univ.
,
8
(
4
), pp.
408
415
.
17.
Lakshminarayana
,
K.
, and
Rao
,
L. B.
,
1984
, “
Graphical Synthesis of the RSSR Crank-Rocker Mechanism
,”
Mech. Mach. Theory
,
19
(
3
), pp.
331
336
.
18.
Liang
,
Z.
,
1995
, “
Computer-Aided Graphical Design of Spatial Mechanisms
,”
Mech. Mach. Theory
,
30
(
2
), pp.
299
312
.
19.
Shen
,
Q.
,
Russell
,
K.
,
Lee
,
W. T.
, and
Sodhi
,
R. S.
,
2011
, “
On Cam System Design to Replicate Spatial Four-Bar Mechanism Coupler Motion
,”
Inverse Probl. Sci. Eng.
,
19
(
2
), pp.
251
265
.
20.
D'Alessio
,
J.
,
Russell
,
K.
,
Lee
,
W. T.
, and
Sodhi
,
R. S.
,
2017
, “
On the Application of Rrss Motion Generation and Rrss Axode Generation for the Design of a Concept Prosthetic Knee
,”
Mech. Based Des. Struct. Mach.
,
45
(
3
), pp.
406
414
.
21.
Shih
,
A. J.
, and
Yan
,
H. S.
,
2002
, “
Synthesis of a Single-Loop, Overconstrained Six Revolute Joint Spatial Mechanism for Two-Position Cylindrical Rigid Body Guidance
,”
Mech. Mach. Theory
,
37
(
1
), pp.
61
73
.
22.
Lin
,
S.
,
Liu
,
J.
,
Wang
,
H.
, and
Zhang
,
Y.
,
2018
, “
A Novel Geometric Approach for Planar Motion Generation Based on Similarity Transformation of Pole Maps
,”
Mech. Mach. Theory
,
122
, pp.
97
112
.
23.
Angeles
,
J.
, and
Bai
,
S.
,
2005
, “
Some Special Cases of the Burmester Problem for Four and Five Poses
,”
ASME
Paper No. DETC2005-84871.
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