###### Abstract  
[PERSON] linkage is an appealing mechanism to implement a bio-inspired motion for a legged robot. The oval orbit that is generated by the [PERSON] linkage, possessing a transversal axis longer than a lateral axis, achieves energy efficient walking comparing to the circular orbit that is generated by the four-bar linkage. However, the ensemble of its links can produce different patterns of orbits other than oval orbits, some of which are not qualified to be the foot trajectories. It is vital to give a guideline, to which one can refer, to ensure the design of a Theo Jansen leg always possessing its eligibility. In this paper, the machine learning technique, called SVM (Support Vector Machine) along with machine vision serving as a classifier to distinguish desired trajectories from undesired ones, is employed and two databases gathering all eligible data concerned with properties of orbits and dimensions of Theo Jansen linkages are established. Based upon SVM to delimit the eligible designs, one can seek the improvement of a Theo Jansen linkage by resizing its links without rendering an ineligible design. The ensemble dimensions of Theo Jansen linkage can be determined by searching the orbits in compliance with the specification of obliqueness and slenderness from the database of properties and using their correspondent identity numbers to list all candidates of TJLs from the database of dimensions. With the aid of this proposed method, the TJLs have been successfully designed and implemented on a legged robot. Theo Jansen linkage; Support Vector Machine; machine vision +
Footnote †: journal: Applied Soft  
some trigonometric constraints. It well defines a forward problem, i.e., given the dimension of the TJL to generate the orbit. Nevertheless, how to design a TJL to achieve locomotion is in fact a sort of inverse problems, i.e., given a specification of orbit to determine the dimension of the TJL. The primary goal of this paper is to develop a technique to design the TJLs, i.e., solving its inverse problem. Conventionally, the standard numerical scheme called LM (Levenberg-Marquardt) method [9; 10] is an effective tool to solve the inverse problems. However, the patterns of orbits produced by the TJL may vary according to its ensemble dimension and can be casted into four groups, such as bell curves, ovals, sharp-pointed ovals, and lemniscates. Some orbits can be used as the foot trajectories for legged robots but some cannot. Overall speaking, the ovals or bell orbits are legitimate and the sharp-pointed ovals are partly legitimate, nevertheless the lemniscates are illegitimate. Although the algorithm of LM always leads to a (locally optimal) solution, it does not guarantee the solution falling into the legitimate class because it is unable to tell the patterns of orbits. Besides, the way of given a prescribed orbit to determine the dimension of a TJL is too strict to be practical. The pattern of foot trajectories is only one factor in designing a legged robot. In general, it demands abundant feasible designs in which a designer can make a trade off when other factors are taken into account. Hence, it is vital to give a guideline, to which one can refer, to ensure that the design of a TJL always possesses its eligibility that is generating a legitimate orbit for a legged robot. In the attempt of gathering feasible designs to establish a database, difficulty arises as to how to distinguish the feasible data from the infeasible ones among a vast amount of data. We propose employing the ML (Machine Learning) technique [11; 12; 13] called SVM (Support Vector Machine) along with machine vision [14; 15] to tackle this problem. There are two merits of using SVM. First, it gives a geometric perspective that is finding the equation for a hyperplane to best separate the different classes in the feature space. Second, it solves the convex optimization problem analytically and hence always returns the same optimal hyperplane. The proposed method is divided into two steps.