This paper presents a procedure that determines the dimensions of two constraining links to be added to a three degree-of-freedom spherical parallel manipulator so that it becomes a one degree-of-freedom spherical (8, 10) eight-bar linkage that guides its end-effector through five task poses. The dimensions of the spherical parallel manipulator are unconstrained, which provides the freedom to specify arbitrary base attachment points as well as the opportunity to shape the overall movement of the linkage. Inverse kinematics analysis of the spherical parallel manipulator provides a set of relative poses between all of the links, which are used to formulate the synthesis equations for spherical RR chains connecting any two of these links. The analysis of the resulting spherical eight-bar linkage verifies the movement of the system.

1.
Burmester
,
L.
, 1888,
Lehrbuch der Kinematik
,
A.
Felix
, ed.,
Verlag
,
Leipzig, Germany
.
2.
Soh
,
G. S.
, and
McCarthy
,
J. M.
, 2007, “
Synthesis of Mechanically Constrained Planar 2-RRR Planar Parallel Robots
,”
Proceedings of the 2007 IFToMM World Congress
,
Besancon
,
France
, Jun. 18–21.
3.
Suh
,
C. H.
, and
Radcliffe
,
C. W.
, 1978,
Kinematics and Mechanisms Design
,
Wiley
,
New York
.
4.
Chen
,
P.
, and
Roth
,
B.
, 1969, “
Design Equations for the Finitely and Infinitesimally Separated Position Synthesis of Binary Links and Combined Link Chains
,”
ASME J. Eng. Ind.
0022-0817,
91
, pp.
209
219
.
5.
McCarthy
,
J. M.
, 2000,
Geometric Design of Linkages
,
Springer-Verlag
,
New York
.
6.
Alizade
,
R. I.
, and
Kilit
,
O.
, 2005, “
Analytical Synthesis of Function Generating Four-Bar Mechanism for Five Precision Points
,”
Mech. Mach. Theory
0094-114X,
40
(
7
), pp.
863
878
.
7.
Hernandez
,
S.
,
Bai
,
S.
, and
Angeles
,
J.
, 2006, “
The Design of a Chain of Spherical Stephenson Mechanisms for a Gearless Robotic Pitch-Roll Wrist
,”
ASME J. Mech. Des.
1050-0472,
128
(
2
), pp.
422
429
.
8.
Ketchel
,
J. S.
, and
Larochelle
,
P. M.
, 2007, “
Computer-Aided Manufacturing of Spherical Mechanisms
,”
Mech. Mach. Theory
0094-114X,
42
(
2
), pp.
131
146
.
9.
Alizade
,
R. I.
, and
Tagiyev
,
N. R.
, and
Duffy
,
J.
, (1994), “
A Forward and Reverse Displacement Analysis of an In-Parallel Spherical Manipulator
,”
Mech. Mach. Theory
0094-114X,
29
(
1
), pp.
125
137
.
10.
Bulca
,
F.
,
Angeles
,
J.
, and
Zsomber-Murray
,
P. J.
, 1999, “
On the Workspace Determination of Spherical Serial and Platform Mechanisms
,”
Mech. Mach. Theory
0094-114X,
34
(
3
), pp.
497
512
.
11.
Hess-Coelho
,
T. A.
, 2007, “
A Redundant Parallel Spherical Mechanism for Robotic Wrist Applications
,”
ASME J. Mech. Des.
1050-0472,
129
(
8
), pp.
891
895
.
12.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2004, “
Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory
,”
ASME J. Mech. Des.
1050-0472,
126
(
1
), pp.
101
108
.
13.
Wang
,
J.
, and
Gosselin
,
C. M.
, 2004, “
Singularity Loci of a Special Class of Spherical 3-DOF Parallel Mechanisms With Prismatic Actuators
,”
ASME J. Mech. Des.
1050-0472,
126
(
2
), pp.
319
326
.
14.
Gallardo
,
J.
,
Rodriguez
,
R.
,
Caudillo
,
M.
, and
Rico
,
J. M.
, 2008, “
A Family of Spherical Parallel Manipulators With Two Legs
,”
Mech. Mach. Theory
0094-114X,
43
(
2
), pp.
201
216
.
15.
Wampler
,
C. W.
, 2004, “
Displacement Analysis of Spherical Mechanisms Having Three or Fewer Loops
,”
ASME J. Mech. Des.
1050-0472,
126
(
1
), pp.
93
100
.
16.
McCarthy
,
J. M.
, 1983, “
Planar and Spatial Rigid Motion as Special Cases of Spherical and 3-Spherical Motion
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
150
(
3
), pp.
569
575
.
17.
Chiang
,
C. H.
, 1988,
Kinematics of Spherical Mechanisms
,
Cambridge University Press
,
Cambridge
, p.
424
.
18.
Tsai
,
L. W.
, 2001,
Enumeration of Kinematic Structures According to Function
,
CRC
,
Bora Raton
.
19.
Yan
,
H. S.
, and
Hung
,
C. C.
, 2006, “
Identifying and Counting the Number of Mechanisms From Kinematic Chains Subject to Design Constraints
,”
ASME J. Mech. Des.
1050-0472,
128
(
9
), pp.
1177
1182
.
20.
Ding
,
H.
, and
Huang
,
Z.
, 2007, “
The Establishment of the Canonical Perimeter Topological Graph of Kinematic Chains and Isomorphis Identification
,”
ASME J. Mech. Des.
1050-0472,
129
(
9
), pp.
915
923
.
21.
McCarthy
,
J. M.
, 1990,
Introduction to Theoretical Kinematics
,
MIT
,
Cambridge, MA
.
You do not currently have access to this content.