Research Papers

A Machine Learning Approach to Kinematic Synthesis of Defect-Free Planar Four-Bar Linkages

[+] Author and Article Information
Shrinath Deshpande

Computer-Aided Design and Innovation Lab,
Department of Mechanical Engineering,
Stony Brook University,
Stony Brook, NY 11794-2300

Anurag Purwar

Computer-Aided Design and Innovation Lab,
Department of Mechanical Engineering,
Stony Brook University,
Stony Brook, NY 11794-2300
e-mail: anurag.purwar@stonybrook.edu

1Corresponding author.

Manuscript received March 29, 2018; final manuscript received December 12, 2018; published online February 4, 2019. Assoc. Editor: Conrad Tucker.

J. Comput. Inf. Sci. Eng 19(2), 021004 (Feb 04, 2019) (10 pages) Paper No: JCISE-18-1078; doi: 10.1115/1.4042325 History: Received March 29, 2018; Revised December 12, 2018

Synthesizing circuit-, branch-, or order-defects-free planar four-bar mechanism for the motion generation problem has proven to be a difficult problem. These defects render synthesized mechanisms useless to machine designers. Such defects arise from the artificial constraints of formulating the problem as a discrete precision position problem and limitations of the methods, which ignore the continuity information in the input. In this paper, we bring together diverse fields of pattern recognition, machine learning, artificial neural network, and computational kinematics to present a novel approach that solves this problem both efficiently and effectively. At the heart of this approach lies an objective function, which compares the motion as a whole thereby capturing designer's intent. In contrast to widely used structural error or loop-closure equation-based error functions, which convolute the optimization by considering shape, size, position, and orientation of the given task simultaneously, this objective function computes motion difference in a form, which is invariant to similarity transformations. We employ auto-encoder neural networks to create a compact and clustered database of invariant motions of known defect-free linkages, which serve as a good initial choice for further optimization. In spite of highly nonlinear parameters space, our approach discovers a wide pool of defect-free solutions very quickly. We show that by employing proven machine learning techniques, this work could have far-reaching consequences to creating a multitude of useful and creative conceptual design solutions for mechanism synthesis problems, which go beyond planar four-bar linkages.

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Fig. 1

The four-bar mechanism obtained using the precision position approach suffers from circuit defect, as no coupler circuit passes through all precision positions

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Fig. 2

The machine learning approach begins by creating an invariant signature for the path and the motion data, which facilitates a compact and hierarchical clustered database and an auto-encoder neural network trained to elicit good, defect-free solutions or subjected to local, fast optimization. The results are defect-free conceptual design solutions for input problems.

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Fig. 3

(a) The path of the input motion along with direction of parametrization and (b) motion components x(t), y(t), θ(t) are plotted against parameter t

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Fig. 4

Curvature and its unsigned integral for the path shown in Fig. 3

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Fig. 5

Path and motion signatures of the motion shown in Fig.3: (a) path signature and (b) motion signature

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Fig. 6

Part path is formed by trimming whole path followed by translation and scaling. Arrows indicate the increasing direction of parameter t.

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Fig. 7

Path signatures of part p and whole W from Fig. 6. The array index i corresponds to the index location for the array of the K. The domain of path signature is scale-invariant but the range still has a scaling factor, which is taken care of by normalized cross-correlation.

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Fig. 8

Normalized cross correlation of the signatures computed along each direction is shown. It can be seen that exact match is found at j =0.

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Fig. 9

Motion signatures of the trajectories shown in Fig. 6. The domain as well as range of motion signature is invariant to similarity transformation.

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Fig. 10

Dissimilarity function of two motion signatures along both directions. It can be seen that the exact match is found at j =0, where the template is fully embedded inside the other motion.

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Fig. 11

Parametric representation of four-bar linkage with all revolute joints. We set l0 = 1 and one fixed joint at the origin of the global frame along with making the fixed length of four-bar parallel to the x-axis.

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Fig. 12

Coupler motions of the four-bar linkage with variation of parameters l1 and l2. It can be seen that motion topology changes from close-loop Grashof to open-loop Triple Rocker.

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Fig. 13

Motion signatures obtained by steps given in Sec. 2. Although topology difference is even more evident in this representation; it also signifies the similarity pattern between them.

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Fig. 14

Distance (Emin) from Eq. (4) as the parameters l1 and l3 are varied. Although open loop breaks at l1:0.55, l3:1.5, there are no spikes of error function in the region near singularity, as the shape is very similar between the two topologies.

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Fig. 15

Probability distribution function used in random sampling for parameters l1, l2, and l3

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Fig. 16

A small-scale version of the auto-encoder. This network takes five-dimensional input in the input layer. At each encoder layer, the input is compressed into a vector of lower dimensions, the lowest at the bottleneck layer.

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Fig. 17

Case study 1: path traced by hip joint during sit-to-stand motion

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Fig. 18

First eight linkages in Table 2 and their resultant coupler paths

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Fig. 19

Case study 2: user-specified motion necessary for the snow shoveling task

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Fig. 20

Case study 2—Query result: motion signatures in the dataset with highest similarity

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Fig. 21

Case study 2: first eight linkages in Table 4 and their resultant coupler motions



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