Single degree-of-freedom coupled serial chain (SDCSC) mechanisms are a class of mechanisms that can be realized by coupling successive joint rotations of a serial chain linkage, by way of gears or cable-pulley drives. Such mechanisms combine the benefits of single degree-of-freedom design and control with the anthropomorphic workspace of serial chains. Our interest is in creating articulated manipulation-assistive aids based on the SDCSC configuration to work passively in cooperation with the human operator or to serve as a low-cost automation solution. However, as single-degree-of-freedom systems, such SDCSC-configuration manipulators need to be designed specific to a given task. In this paper, we investigate the development of a synthesis scheme, leveraging tools from Fourier analysis and optimization, to permit the end-effectors of such manipulators to closely approximate desired closed planar paths. In particular, we note that the forward kinematics equations take the form of a finite trigonometric series in terms of the input crank rotations. The proposed Fourier-based synthesis method exploits this special structure to achieve the combined number and dimensional synthesis of SDCSC-configuration manipulators for closed-loop planar path-following tasks. Representative examples illustrate the application of this method for tracing candidate square and rectangular paths. Emphasis is also placed on conversion of computational results into physically realizable mechanism designs.

Keywords:
manipulator kinematics, end effectors, position control, Fourier analysis, optimisation, closed loop systems
Topics:
Chain, Design, End effectors, Fourier analysis, Kinematics, Manipulators, Optimization, Degrees of freedom, Computer software, Pulleys
1.
Krovi, V., 1998, “Design and Virtual Prototyping of User-Customized Assistive Devices,” Ph.D. thesis, Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA.
2.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press, Oxford.
3.
Nie, X., and Krovi, V., 2001, “Design of Passive Reconfigurable Manipulation Assistive Aids,” DETC2001/DAC-21087, Proceedings of the 2001 ASME Design Engineering Technical Conferences, Pittsburgh, PA.
4.
Nie, X., 2001, “Design of Reconfigurable Manipulation Assist Aids by Fourier Methods,” M.Eng. thesis, Department of Mechanical Engineering, McGill University, Montreal, Canada.
5.
Sandor, G. N., 1964, “On the Existence of a Cycloidal Burmester Theory in Planar Kinematics,” Trans. ASME, 31, J. Appl. Mech., 86, pp. 694–699.
6.
Wunderlich, W., 1970, “Chapter 33: Hohere Radlinien,” Ebene Kinematik, B.I-Hochschultaschenbucher, No. 447/447A, Mannheim, Germany.
7.
Kaufman
,
R. E.
, and
Sandor
,
G. N.
,
1969
, “
Bicycloidal Crank: A New Four-Link Mechanism
,”
Trans. ASME, J. Eng. Ind.
,
91
, pp.
91
–
96
.
8.
Tsai
,
L.-W.
,
1995
, “
Design of Tendon-Driven Manipulators
,”
ASME J. Mech. Des.
,
117
, pp.
80
–
86
.
9.
Rosheim
,
M.
,
1997
, “
In the Footsteps of Leonardo
,”
IEEE Rob. Autom. Mag.
,
4
, pp.
12
–
14
.
10.
Leaver
,
S.
,
McCarthy
,
J. M.
, and
Bobrow
,
J.
,
1988
, “
The Design and Control of a Robot Finger for Tactile Sensing
,”
J. Rob. Syst.
,
5
, pp.
567
–
581
.
11.
Figliolini, G., and Ceccarelli, M., 1998, “A Motion Analysis for One D.O.F. Anthropomorphic Finger Mechanism,” DETC98/MECH-5985, Proceedings of the 1998 ASME Design Engineering Technical Conferences, Atlanta, GA.
12.
Hong
,
D. W.
, and
Cipra
,
R. J.
,
2003
, “
A Method for Representing the Configuration and Analyzing the Motion of Complex Cable-Pulley Systems
,”
ASME J. Mech. Des.
,
125
, pp.
332
–
341
.
13.
Sandor, G. N., and Erdman, A. G., 1984, Advanced Mechanism Design: Analysis and Synthesis, Vol. 2, Prentice-Hall, Englewood Cliffs, NJ.
14.
Rao, S. S., 2004, Mechanical Vibrations, 4th ed., Prentice-Hall, Upper Saddle River, NJ.
15.
Thomson, W. T., and Dahleh, M. D., 1998, Theory of Vibration With Applications, 5th ed., Prentice-Hall, Upper Saddle River, NJ.
16.
Lin
,
C.-C.
,
2002
, “
Finite Element Analysis of a Computer Hard Disk Drive Under Shock
,”
ASME J. Mech. Des.
,
124
, pp.
121
–
125
.
17.
Yu
,
S. D.
, and
Xi
,
F.
,
2003
, “
Free Vibration Analysis of Planar Flexible Mechanisms
,”
ASME J. Mech. Des.
,
125
, pp.
764
–
772
.
18.
Yuan
,
L.
, and
Rastegar
,
J.
,
2004
, “
Kinematics Synthesis of Linkage Mechanisms With Cam Integrated Joints for Controlled Harmonic Content of the Output Motion
,”
ASME J. Mech. Des.
,
126
, pp.
135
–
142
.
19.
Rastegar
,
J.
, and
Yuan
,
L.
,
2002
, “
A Systematic Method for Kinematics Synthesis of High-Speed Mechanisms With Optimally Integrated Smart Materials
,”
ASME J. Mech. Des.
,
124
, pp.
14
–
20
.
20.
Ullah
,
I.
, and
Kota
,
S.
,
1997
, “
Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods
,”
ASME J. Mech. Des.
,
119
, pp.
504
–
510
.
21.
Oppenheim, A. V., and Schafer, R. W., 1992, Discrete-Time Signal Processing, Prentice Hall, Englewood Cliffs, NJ.
22.
Angeles, J., and Liu, Z., 1993, in Modern Kinematics: Developments in the Last Forty Years, edited by A. G. Erdman, John Wiley & Sons, New York.
23.
Chedmail, P., 1998, “Chapter I-5: Optimization of Multi-DOF Mechanisms,” Computational Methods in Mechanical Systems: Mechanism Analysis, Synthesis and Optimization, Springer, Berlin.
24.
Krovi
,
V.
,
Ananthasuresh
,
G. K.
, and
Kumar
,
V.
,
2002
, “
Kinematic and Kinetostatic Synthesis of Planar Coupled Serial Chain Mechanisms
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
301
–
312
.
25.
Krovi
,
V.
,
Ananthasuresh
,
G. K.
, and
Kumar
,
V.
,
2001
, “
Kinematic Synthesis of Spatial R-R Dyads for Path Following With Applications to Coupled Serial Chain Mechanisms
,”
ASME J. Mech. Des.
,
123
, pp.
359
–
366
.
26.
Zhou
,
H.
, and
Cheung
,
H. M.
,
2001
, “
Optimal Synthesis of Crank-Rocker Linkages for Path Generation Using the Orientation Structural Error of the Fixed Link
,”
Mech. Mach. Theory
,
36
, pp.
973
–
982
.
27.
Zhou
,
H.
, and
Ting
,
K.-L.
,
2002
, “
Adjustable Slider-Crank Linkages for Multiple Path Generation
,”
Mech. Mach. Theory
,
37
, pp.
499
–
509
.
28.
Vanderplaats, G. N., 1982, “Chapter 3: Unconstrained Optimization in N Variables,” Numerical Optimization Techniques in Engineering Design: With Applications, McGraw-Hill, New York.
29.
Farin, G., 1997, Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide, 4th ed., Academic Press, San Diego, CA.
30.
Pang, Y.-W., 1999, “Fourier Methods for Synthesis of Coupled Serial Chain Mechanisms,” Honors thesis, Department of Mechanical Engineering, McGill University, Montreal, Canada.
Copyright © 2005
 by ASME
You do not currently have access to this content.