This paper presents a methodology for synthesizing planar linkages to approximate any prescribed periodic function. The mechanisms selected for this task are the slider-crank and the geared five-bar with connecting rod and sliding output (GFBS), where any number of double-crank (or drag-link) four-bars are used as drivers. A slider-crank mechanism, when comparing the input crank rotation to the output slider displacement, produces a sinusoid-like function. Instead of directly driving the input crank, a drag-link four-bar may be added to drive the crank from its output via a rigid connection between the two. Driving the input of the added four-bar results in a function that modifies the sinusoid-like curve. This process can be continued through the addition of more drag-link mechanisms to the device, progressively altering the curve toward any periodic function with a single maximum. For periodic functions with multiple maxima, a GFBS is used as the terminal linkage added to the chain of drag-link mechanisms. The synthesis process starts by analyzing one period of the function to design either the terminal slider-crank or terminal GFBS. matlab's fmincon command is then utilized as the four-bars are added to reduce the structural error between the desired function and the input–output function of the mechanism. Mechanisms have been synthesized in this fashion to include a large number of links that are capable of closely producing functions with a variety of intriguing features.

References

References
1.
Erdman
,
A.
,
Sandor
,
G.
, and
Kota
,
S.
,
2001
,
Mechanism Design: Analysis and Synthesis
,
4th ed.
,
Prentice Hall
, Upper Saddle River, NJ.
2.
Norton
,
R. L.
,
2012
,
Design of Machinery
,
5th ed.
,
McGraw Hill
,
New York
.
3.
McCarthy
,
J. M.
and
Soh
,
G. S.
,
2011
,
Geometric Design of Linkages
(Interdisciplinary Applied Mathematics),
2nd ed.
,
Springer
,
New York
.
4.
Waldron
,
K. J.
, and
Kinzel
,
G. L.
,
2004
,
Kinematics, Dynamics, and Design of Machinery
,
2nd ed.
,
Wiley
,
Hoboken, NJ
.
5.
Almandeel
,
A.
,
Murray
,
A. P.
,
Myszka
,
D. H.
, and
Stumph
,
H. E.
, III
,
2015
, “
A Function Generation Synthesis Methodology for All Defect-Free Slider-Crank Solutions for Four Precision Points
,”
ASME J. Mech. Rob.
,
7
(
3
), p.
031020
.
6.
Freudenstein
,
F.
,
1954
, “
An Analytical Approach to the Design of Four-Link Mechanisms
,”
Trans. ASME
,
76
, pp.
483
492
.
7.
Erdman
,
A.
,
Sandor
,
G.
, and
Kota
,
S.
,
1984
,
Advanced Mechanism Design: Analysis and Synthesis
, Vol.
2
,
Prentice Hall
, Englewood Cliffs, NJ.
8.
Freudenstein
,
F.
,
1959
, “
Structural Error Analysis in Plane Kinematic Synthesis
,”
J. Eng. Ind.
,
81
(
1
), pp.
15
22
.
9.
Naik
,
D.
, and
Amarnath
,
C.
,
1989
, “
Synthesis of Adjustable Four Bar Function Generators Through Five Bar Loop Closure Equations
,”
Mech. Mach. Theory
,
24
(
6
), pp.
523
526
.
10.
McGovern
,
J. F.
, and
Sandor
,
G. N.
,
1973
, “
Kinematic Synthesis of Adjustable Mechanisms—Part 1: Function Generation
,”
ASME J. Manuf. Sci. Eng.
,
95
(
2
), pp.
417
422
.
11.
Soong
,
R.-C.
, and
Chang
,
S.-B.
,
2011
, “
Synthesis of Function-Generation Mechanisms Using Variable Length Driving Links
,”
Mech. Mach. Theory
,
46
(
11
), pp.
1696
1706
.
12.
Subbian
,
T.
, and
Flugrad
,
D.
,
1994
, “
Six and Seven Position Triad Synthesis Using Continuation Methods
,”
ASME J. Mech. Des.
,
116
(
2
), pp.
660
665
.
13.
McLarnan
,
C.
,
1963
, “
Synthesis of Six-Link Plane Mechanisms by Numerical Analysis
,”
ASME J. Manuf. Sci. Eng.
,
85
(
1
), pp.
5
10
.
14.
Dhingra
,
A. K.
,
Cheng
,
J. C.
, and
Kohli
,
D.
,
1994
, “
Synthesis of Six-Link, Slider-Crank and Four-Link Mechanisms for Function, Path and Motion Generation Using Homotopy and m-Homogenization
,”
ASME J. Mech. Des.
,
116
(
4
), pp.
1122
1131
.
15.
Dhingra
,
A. K.
, and
Mani
,
N. K.
,
1993
, “
Finitely and Multiply Separated Synthesis of Link and Geared Mechanisms Using Symbolic Computing
,”
ASME J. Mech. Des.
,
115
(
3
), pp.
560
567
.
16.
Al-Dwairi
,
A. F.
,
2009
, “
Design of Centric Drag-Link Mechanisms for Delay Generation With Focus on Space Occupation
,”
ASME J. Mech. Des.
,
131
(
1
), p.
011015
.
17.
Oleksa
,
S. A.
, and
Tesar
,
D.
,
1971
, “
Multiply Separated Position Design of the Geared Five-Bar Function Generator
,”
ASME J. Manuf. Sci. Eng.
,
93
(
1
), pp.
74
84
.
18.
Erdman
,
A. G.
, and
Sandor
,
G. N.
,
1971
, “
Kinematic Synthesis of a Geared Five-Bar Function Generator
,”
ASME J. Manuf. Sci. Eng.
,
93
(
1
), pp.
11
16
.
19.
Sultan
,
I.
, and
Kalim
,
A.
,
2011
, “
On the Kinematics and Synthesis of a Geared Five-Bar Slider-Crank Mechanism
,”
Proc. Inst. Mech. Eng. C
,
225
(
5
), pp.
1253
1261
.
20.
Freudenstein
,
F.
, and
Primrose
,
E.
,
1963
, “
Geared Five-Bar Motion—Part I: Gear Ratio Minus One
,”
ASME J. Appl. Mech.
,
30
(
2
), pp.
161
169
.
21.
Primrose
,
E.
, and
Freudenstein
,
F.
,
1963
, “
Geared Five-Bar Motion—Part 2: Arbitrary Commensurate Gear Ratio
,”
ASME J. Appl. Mech.
,
30
(
2
), pp.
170
175
.
22.
Artobolevskii
,
I. I.
,
1964
,
Mechanisms for the Generation of Plane Curves
,
Macmillan
,
New York
.
23.
Lui
,
Y.
, and
McCarthy
,
J. M.
,
2016
, “
Design of Mechanisms to Trace Plane Curves
,”
ASME
Paper No. DETC2016-59689.
24.
Sutherland
,
G.
, and
Roth
,
B.
,
1975
, “
An Improved Least-Squares Method for Designing Function-Generating Mechanisms
,”
ASME J. Manuf. Sci. Eng.
,
97
(
1
), pp.
303
307
.
25.
Chen
,
F.
, and
Chan
,
V.-L.
,
1974
, “
Dimensional Synthesis of Mechanisms for Function Generation Using Marquardt's Compromise
,”
ASME J. Manuf. Sci. Eng.
,
96
(
1
), pp.
131
137
.
26.
Sarganachari
,
S. G.
,
Math
,
V. B.
, and
Ali
,
S. A.
,
2010
, “
Synthesis of Planar Six-Bar Mechanism for Function Generation: A Variable Topology Approach
,”
Int. J. Appl. Eng. Res.
,
5
(
3
), pp.
471
476
.
27.
Shariati
,
M.
, and
Norouzi
,
M.
,
2011
, “
Optimal Synthesis of Function Generator of Four-Bar Linkages Based on Distribution of Precision Points
,”
Meccanica
,
46
(
5
), pp.
1007
1021
.
28.
Akcali
,
I.
, and
Dittrich
,
G.
,
1989
, “
Function Generation by Galerkin's Method
,”
Mach. Mech. Theory
,
24
(
1
), pp.
39
43
.
29.
Ting
,
K.-L.
,
1994
, “
Mobility Criteria of Geared Five-Bar Linkages
,”
Mech. Mach. Theory
,
29
(
2
), pp.
251
264
.
30.
Murray
,
A. P.
, and
Larochelle
,
P.
,
1998
, “
A Classification Scheme for Planar 4R, Spherical 4R, and Spatial RCCC Linkages to Facilitate Computer Animation
,”
ASME
Paper No. DETC98/MECH-5887.
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