Closed chain mechanisms are used as robotic manipulators with special features. A planar two-DOF closed loop mechanism provides desired position of an end effecter in a confined workspace with two input motions. Position of end effecter depends on various factors including joint clearance. Positional accuracy forms important parameter for kinematic analysis of mechanism. This paper presents simple approach for quantifying error due to joint clearance in a two-DOF mechanism. Generalized scheme for positional deviation with and without clearance at joint is presented. Orientation of clearance links for maximum positional error is identified. Error at various positions is quantified in relation with clearance link length. Computer programming is used as a tool to workout positional analysis of mechanism. Results show that error is independent of magnitude of clearance, however, a function of location of end effecter in workspace.

References

1.
Gergorio Raffale
,
Di.
, and
Castelli
,
V. P.
, 2001, “
Position Analysis in Analytical Form of 3-PSP Mechanism
,”
ASME J. Mech. Des.
,
123
, pp.
51
57
.
2.
Cameron
,
S.
, 1990, “
Stiffness Mapping for Parallel Manipulators
,”
IEEE Trans. Robot. Autom.
,
6
(
3
), pp.
377
382
.
3.
Ecorechard
,
G.
, and
Maurine
,
P.
, 2004, “
Self Calibration of Delta Robots With Elastic Deformation Compensations
,”
IEEE International Conference on Robotics and Automation (ICRA’04)
.
4.
Zhongchao
,
S.
,
Tianxiang
,
Y.
,
Weimin
,
C.
, and
Bifeng
,
S.
, 2011, “
Reliability Analysis for Close Position Accuracy of Gear Door Mechanism Based on Importance Sampling
,”
International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (ICQR2MSE)
, pp.
168
172
.
5.
Wang
,
Z.
,
Zhao
,
Z.
,
Pang
,
Z.
, and
Zhang
,
C.
, 2011, “Kinematics Analysis and Simulation of a New 3 Degrees of Freedom Spatial Robot Mechanism Composed by Closed Chain,” Second International Conference on Mechanic Automation and Control Engineering (MACE), pp. 1373–1376.
6.
Olivier
,
C.
,
Pierrot
,
F.
,
Krut
,
S.
,
Baradat
,
C.
, and
Nabat
,
V.
, 2011, “
Par2: A Spatial Mechanism for Fast Planar Two-Degree-of-Freedompick-and-Place Applications
,”
Meccanica
,
46
(
1
), pp.
239
248
.
7.
Junfu
,
Z.
, and
Xiaoping
,
D.
, 2011, “
Time-Dependent Reliability Analysis for Function Generator Mechanisms
,”
ASME J. Mech. Des.
,
133
(
3
), p.
031005
.
8.
Fu-Chen
,
C.
,
Yih-Fong
,
T.
,
Meng-Hui
,
H.
, and
Wei-Ren
,
C.
, 2010, “
Combining Taguchi Method, Principal Component Analysis and Fuzzy Logic to the Tolerance Design of a Dual Purpose Six Bar Mechanism
,”
Trans. Can. Soc. Mech. Eng.
,
34
(
2
), pp.
277
293
.
9.
Xiaoping
D.
,
Pavan Kumar
V.
, and
Deshun
L.
, 2009, “
Robust Mechanism Synthesis With Random and Interval Variables
,”
Mech. Mach. Theory
,
44
(
7
), pp.
1321
1337
.
10.
Jun
W.
, and
Anurag Purwar
,
Q. J. Ge.
, 2010, “
Interactive Dimensional Synthesis and Motion Design of Planar 6R Single-Loop Closed Chains via Constraint Manifold Modification
,”
J. Mech. Robot.
,
2
, p.
031012
.
11.
Rhyu
,
J. H.
, and
Kwak
,
B. M.
, 1988, “
Optimal Stochastic Design of Four-Bar Mechanisms for Tolerance and Clearance
,”
ASME J. Mech., Trans., Autom. Des.
,
110
, pp.
255
262
.
12.
Garrett
,
R. E.
, and
Hall
,
A. S.
, Jr.
1969, “
Effect of Tolerance and Clearance in Linkage Design
,”
ASME J. Eng. Ind.
,
91
, pp.
198
202
.
13.
Sharfi
,
O. M. A.
, and
Smith
,
M. R.
, 1983, “
A Simple Method for the Allocation of Appropriate Tolerances and Clearances in Linkage Mechanisms
,”
Mech. Mach. Theory
,
18
(
2
), pp.
123
129
.
14.
Tsai
,
M.-J.
, and
Lai
,
T. H.
, 2004, “
Kinematic Sensitivity Analysis of Linkage With Joint Clearance Based on Transmission Quality
,”
Mech. and Mach. Theory
,
39
, pp.
1189
1206
.
15.
Chakraborty
,
J.
, 1975, “
Synthesis of Mechanical Error in Linkages
,”
Mech. Mach. Theory
,
10
, pp.
155
165
.
16.
Dhande
,
S. G.
, and
Chakraborty
,
J.
, 1973, “
Analysis and Synthesis of Mechanical Error in Linkages—A Stochastic Approach
,”
ASME J. Eng. Ind.
,
95
, pp.
672
676
.
17.
Lee
,
S. J.
,
Gilmore
,
B. J.
, and
Otto
,
M. M.
, 1993, “
Dimensional Tolerance Allocation of Stochastic Dynamic Mechanical Systems Through Performance and Sensitivity Analysis
,”
ASME J. Mech. Des.
,
115
, pp.
392
402
.
18.
Takaaki
,
O.
, 2005, “
Error Compensation System for Joints, Links and Machine Frame of Parallel Kinematics Machines
,”
Int. J. Robot. Res.
,
24
, pp.
1087
1102
.
19.
Leu
,
M. C.
,
Dukovski
,
V.
, and
Wang
,
K. K.
, 1987, “
Effect of Mechanical Compliance on Deflection of Robot Manipulators
,”
CIRP Ann.-Manuf. Technol.
,
36
(
1
), pp.
305
309
.
20.
Selcuk
,
E.
, and
Ibrahim
,
U.
, 2009, “
Determining Link Parameters Using Genetic Algorithm in Mechanisms With Joint Clearance
,”
Mech. Mach. Theory
,
44
(
1
), pp.
222
234
.
21.
Mutawe
,
S
,
Yahia
,
M.
, Al-Smadi, and
Sodhi
,
R.
, 2011, “
Planar Four-bar Path Generation Considering Worst Case Joint Tolerances
,”
Proceedings of the World Congress on Engineering and Computer Science 2011(WCECS 2011)
, Vol.
1
, pp.
377
381
.
22.
Zhu
,
J.
, and
Ting
,
K. L.
, 2000, “
Uncertainty Analysis of Planar and Spatial Robots With Joint Clearances
,”
Mech. Mach. Theory
,
35
(
9
), pp.
1239
1256
.
23.
Tsai
,
M. J.
, and
Lai
,
T. H.
, 2008, “
Accuracy Analysis of a Multi-Loop Linkage With Joint Clearances
,”
Mech. Mach. Theory
,
43
(
9
), pp.
1141
1157
.
24.
Selcuk
,
E.
, and
Ibrahim
,
U.
, 2009, “
Investigation on Effect of Joint Clearance on Dynamics of Four-Bar Mechanism
,”
Nonlinear Dyn.
,
58
, pp.
179
198
.
25.
Liu
,
T. S.
, and
Lin
,
Y. S.
, 1990, “
Dynamic Analysis of Flexible Linkages With Lubricated Joints
,”
J. Sound Vib.
,
141
(
2
), pp.
193
205
.
26.
Flores
,
P.
,
Lankarani
,
H. M.
,
Ambrósio
,
J.
, and
Claro
,
J. C. P.
, 2004, “
Modeling Lubricated Revolute Joints in Multibody Mechanical Systems
,”
Proceedings of the Institution of Mechanical Engineers, Part-K
, J. Multi-body Dyn.,
218
, pp.
183
190
.
27.
Ravn
,
P.
,
Shivaswamy
,
S.
,
Alshaer
,
B. J.
, and
Lankarani
,
H. M.
, 2000, “
Joint Clearances With Lubricated Long Bearings in Multibody Mechanical Systems
,”
ASME J. Mech. Des.
,
122
, pp.
485
488
.
28.
Haines
,
R. S.
, 1980, “
Survey: 2-Dimensional Motion and Impact at Revolute Joints
,”
Mech. Mach. Theory
,
15
, pp.
361
370
.
29.
Flores
,
P.
,
Ambrosio
,
J.
,
Claro
,
J. C. P.
,
Lankarani
,
H. M.
,
Koshy
,
C. S.
, 2006, “
A Study on Dynamics of Mechanical Systems Including Joints With Clearance and Lubrication
,”
Mech. Mach. Theory
,
41
(
3
), pp.
247
261
.
30.
Rhee
,
J.
, and
Akay
,
A.
, 1996, “
Dynamic Response of a Revolute Joint With Clearance
,”
Mech. Mach. Theory
,
31
(
1
), pp.
121
134
.
31.
Kolhatkar
,
S. A.
, and
Yajnik
,
K. S.
, 1970, “
The Effects of Play in the Joints of a Function-Generating Mechanism
,”
J. Mech.
5
(
4
), pp.
521
532
.
32.
Ting
,
K. L.
,
Zhu
,
J.
, and
Watkins
,
D.
, 2000, “
The Effects of Joint Clearance on Position and Orientation Deviation of Linkages and Manipulators
,”
Mech. Mach. Theory
,
35
(
3
), pp.
391
401
.
33.
Erdman
,
A. C.
, and
Sandor
,
G. N.
, 1988,
Mechanical Design: Analysis and Synthesis-Volume I
, 2nd ed.,
Prentice Hall of India
,
Connaught Circus, New Delhi
, Chap. I, p.
17
.
You do not currently have access to this content.