Abstract

This paper brings together computer vision, mechanism synthesis, and machine learning to create an image-based variational path synthesis approach for linkage mechanisms. An image-based approach is particularly amenable to mechanism synthesis when the input from mechanism designers is deliberately imprecise or inherently uncertain due to the nature of the problem. In addition, it also lends itself naturally to the creation of a unified approach to mechanism synthesis for different types of mechanisms, since for example, images are formed from a collection of pixels, which themselves could be generated from a four-bar or six-bar. Path synthesis problems have generally been solved for a set of precision points on the intended path such that the designed mechanism passes through those points. This approach usually leads to a small set of over-fitted solutions to particular precision points. However, most kinematic synthesis problems are concept generation problems, where a designer cares more about generating a large number of plausible solutions, which could reach given precision points only approximately. This paper models the input curve as a probability distribution of image pixels and employs a probabilistic generative model to capture the inherent uncertainty in the input. In addition, it gives feedback on the input quality and provides corrections for a more conducive input. The image representation allows for capturing local spatial correlations, which plays an important role in finding a variety of solutions with similar semantics as the input curve. This approach is also conducive to implementation for pressure-sensitive touch-based design interfaces, where the input is not a zero-thickness curve, but the sweep of a small patch on the finger.

References

References
1.
Sandor
,
G. N.
, and
Erdman
,
A. G.
1997
,
Advanced Mechanism Design: Analysis and Synthesis
, Vol.
2
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
2.
McCarthy
,
J. M.
, and
Soh
,
G. S.
,
2010
,
Geometric Design of Linkages
, Vol.
11
,
Springer
,
New York
.
3.
Suh
,
C. H.
, and
Radcliffe
,
C. W.
,
1978
,
Kinematics and Mechanism Design
,
John Wiley and Sons
,
New York
.
4.
Hartenberg
,
R. S.
, and
Denavit
,
J.
,
1964
,
Kinematic Synthesis of Linkages
,
McGraw-Hill
,
New York
.
5.
Lohse
,
P.
,
2013
,
Getriebesynthese: Bewegungsablufe Ebener Koppelmechanismen
,
Springer-Verlag
,
Berlin
.
6.
Hunt
,
K.
,
1978
,
Kinematic Geometry of Mechanisms
,
Clarendon Press
,
Oxford
.
7.
Deshpande
,
S.
, and
Purwar
,
A.
,
2017
, “
A Task Driven Approach to Optimal Synthesis of Planar Four-bar Linkages for Extended Burmester Problem
,”
ASME. J. Mech. Rob.
,
9
(
6
), p.
061005
. 10.1115/1.4037801
8.
Ge
,
Q. J.
,
Purwar
,
A.
,
Zhao
,
P.
, and
Deshpande
,
S.
,
2016
, “
A Task Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds
,”
ASME J. Comput. Inform. Sci. Eng.
,
17
(
3
), p.
031011
. 10.1115/1.4035528
9.
Purwar
,
A.
,
Deshpande
,
S.
, and
Ge
,
Q. J.
,
2017
, “
MotionGen: Interactive Design and Editing of Planar Four-Bar Motions Via a Unified Framework for Generating Pose- and Geometric-Constraints
,”
ASME. J. Mech. Rob.
,
9
(
2
), p.
024504
. 10.1115/1.4035899
10.
Deshpande
,
S.
, and
Purwar
,
A.
,
2019
, “
Computational Creativity Via Assisted Variational Synthesis of Mechanisms Using Deep Generative Models
,”
ASME. J. Mech. Des.
,
141
(
12
), p.
121402
. 10.1115/1.4044396
11.
Deshpande
,
S.
, and
Purwar
,
A.
,
2019
, “
A Machine Learning Approach to Kinematic Synthesis of Defect-Free Planar Four-Bar Linkages
,”
ASME J. Comput. Infor. Sci. Engin.
,
19
(
2
), p.
021004
. 10.1115/detc2018-85578
12.
Nolle
,
H.
, and
Hunt
,
K. H.
,
1971
, “
Optimum Synthesis of Planar Linkages to Generate Coupler Curves
,”
J. Mech.
,
6
(
3
), p.
267
. 10.1016/0022-2569(71)90370-3
13.
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
(
4
), pp.
504
510
. 10.1115/1.2826396
14.
Wu
,
J.
,
Ge
,
Q. J.
,
Gao
,
F.
, and
Guo
,
W. Z.
,
2011
, “
On the Extension of a Fourier Descriptor Based Method for Planar Four-Bar Linkage Synthesis for Generation of Open and Closed Paths
,”
ASME J. Mech. Robot.
,
3
(
3
), p.
031002
. 10.1115/1.4004227
15.
Buskiewicz
,
J.
,
Starosta
,
R.
, and
Walczak
,
T.
,
2009
, “
On the Application of the Curve Curvature in Path Synthesis
,”
Mech. Mach. Theory.
,
44
(
6
), pp.
1223
1239
. 10.1016/j.mechmachtheory.2008.08.001
16.
Khan
,
N.
,
Ullah
,
I.
, and
Al-Grafi
,
M.
,
2015
, “
Dimensional Synthesis of Mechanical Linkages Using Artificial Neural Networks and Fourier Descriptors
,”
Mech. Sci.
,
6
(
1
), pp.
29
34
. 10.5194/ms-6-29-2015
17.
Forsyth
,
D. A.
, and
Ponce
,
J.
,
2002
,
Computer Vision: a Modern Approach
,
Prentice Hall Professional Technical Reference
,
New York City
.
18.
Krizhevsky
,
A.
,
Sutskever
,
I.
, and
Hinton
,
G. E.
,
2012
, “
Imagenet Classification With Deep Convolutional Neural Networks
,”
Adv. Neural inform. Process. Syst.
, pp.
1097
1105
. 10.1145/3065386
19.
Bottou
,
L.
,
2010
, “
Large-Scale Machine Learning With Stochastic Gradient Descent
,”
Proceedings of COMPSTAT’2010
,
Paris
.
20.
Rumelhart
,
D. E.
,
Hinton
,
G. E.
, and
Williams
,
R. J.
,
1986
, “
Learning Representations by Back-Propagating Errors
,”
Nature
,
323
(
6088
), pp.
533
536
. 10.1038/323533a0
21.
Kingma
,
D. P.
, and
Welling
,
M.
,
2014
, “
Auto-Encoding Variational Bayes
,”
Comput. Res. Repository
,
abs/1312.6114
.
22.
Blei
,
D. M.
,
Kucukelbir
,
A.
, and
McAuliffe
,
J. D.
,
2017
, “
Variational Inference: A Review for Statisticians
,”
J. Am. Stat. Assoc.
,
112
(
518
), pp.
859
877
. 10.1080/01621459.2017.1285773
23.
Kullback
,
S.
, and
Leibler
,
R. A.
,
1951
, “
On Information and Sufficiency
,”
Ann. Math. Stat.
,
22
(
1
), pp.
79
86
. 10.1214/aoms/1177729694
You do not currently have access to this content.