This paper deals with the problem of integrated joint type and dimensional synthesis of planar four-bar and six-bar linkages, which could contain both revolute (R) and prismatic (P) joints, for guiding through five specified task positions of the end-effector. In a recent work, we developed a simple algorithm for analyzing a set of given task positions to determine all feasible planar dyads with revolute and/or prismatic joints that can be used to guide through the given positions. This paper extends this algorithm to the integrated joint type and dimensional synthesis of Watt I and II and Stephenson I, II, and III six-bar linkages that contain both R- and P-joints. In the process, we developed a new classification for planar six-bar linkages according to whether the end-effector can be constrained by two dyads (type I), one dyad (type II), or no dyad (type III). In the end, we demonstrate this task-driven synthesis approach with three examples including a novel six-bar linkage for lifting an individual with age disability from seating position to standing position.

Cable-driven parallel robots (CDPRs) are a kind of mechanism with large workspace, fast response, and low inertia. However, due to the existence of various sources of error, it is unavoidable to bring uncertain cable lengths and lead to pose errors of the end-effector. The inverse kinematic model of a CDPR for picking up medicines is established by considering radii of fixed pulleys. The influence of radii of fixed pulleys on errors of cable lengths is explored. Error transfer model of the CDPR is constructed, and uncertain sources of cable lengths are analyzed. Based on evidence theory and error transfer model, an evidence theory-based uncertainty analysis method (ETUAM) is presented. The structural performance function for kinematic response is derived based on the error transfer model. Belief and plausibility measures of joint focal elements under the given threshold are obtained. Kinematic error simulations show that errors of cable lengths become larger with the increase of radii of fixed pulleys. Compared with the vertex method and Monte Carlo method, numerical examples demonstrate the accuracy and efficiency of the ETUAM when it comes to the kinematic uncertainty analysis of the CDPR.

It has been well established that kinematic mapping theory could be applied to mechanism synthesis, where discrete motion approximation problem could be converted to a surface fitting problem for a group of discrete points in hyperspace. In this paper, we applied kinematic mapping theory to planar discrete motion synthesis of an arbitrary number of approximated poses as well as up to four exact poses. A simultaneous type and dimensional synthesis approach is presented, aiming at the problem of mixed exact and approximate motion realization with three types of planar dyad chains (RR, RP, and PR). A two-step unified strategy is established: first N given approximated poses are utilized to formulate a general quadratic surface fitting problem in hyperspace, then up to four exact poses could be imposed as pose-constraint equations to this surface fitting system such that they could be strictly satisfied. The former step, the surface fitting problem, is converted to a linear system with two quadratic constraint equations, which could be solved by a null-space analysis technique. On the other hand, the given exact poses in the latter step are formulated as linear pose-constraint equations and added back to the system, where both type and dimensions of the resulting optimal dyads could be determined by the solution. These optimal dyads could then be implemented as different types of four-bar linkages or parallel manipulators. The result is a novel algorithm that is simple and efficient, which allows for N-pose motion approximation of planar dyads containing both revolute and prismatic joints, as well as handling of up to four prescribed poses to be realized precisely.

This paper studies the problem of spherical four-bar motion synthesis from the viewpoint of acquiring circular geometric constraints from a set of prescribed spherical poses. The proposed approach extends our planar four-bar linkage synthesis work to spherical case. Using the image space representation of spherical poses, a quadratic equation with ten linear homogeneous coefficients, which corresponds to a constraint manifold in the image space, can be obtained to represent a spherical RR dyad. Therefore, our approach to synthesizing a spherical four-bar linkage decomposes into two steps. First, find a pencil of general manifolds that best fit the task image points in the least-squares sense, which can be solved using singular value decomposition (SVD), and the singular vectors associated with the smallest singular values are used to form the null-space solution of the pencil of general manifolds; second, additional constraint equations on the resulting solution space are imposed to identify the general manifolds that are qualified to become the constraint manifolds, which can represent the spherical circular constraints and thus their corresponding spherical dyads. After the inverse computation that converts the coefficients of the constraint manifolds to the design parameters of spherical RR dyad, spherical four-bar linkages that best navigate through the set of task poses can be constructed by the obtained dyads. The result is a fast and efficient algorithm that extracts the geometric constraints associated with a spherical motion task, and leads naturally to a unified treatment for both exact and approximate spherical motion synthesis.

For patients who need lower-limb kinetism rehabilitation training, this paper proposes an effective data-driven approach seeking the design of 1-degree-of-freedom (DOF) six-bar rehab mechanism through gait prediction by body parameters. First, gait trajectories from 79 healthy volunteers are collected along with their body parameters. Then, the normalized gait samples are clustered and regressed into a limited number of representative trajectories with K-means algorithm, and the cluster index is recorded as the label for each trajectory. Next, a genetic-algorithm-optimized support vector machine method is adopted to establish a classifier for the trajectories, obtaining the correspondence between body parameters and cluster labels of gait trajectories. As a result, once a group of body parameters are input into the classifier, the suitable gait trajectory can be predicted for the specific patient. A GA-BFGS algorithm is developed for 1-DOF six-bar mechanism synthesis and a GUI design software is presented that shows how the data-driven design process is realized. The novelty of this paper is using clustering and prediction technique to accomplish the patient-mechanism matching, so that simple, low-priced 1-DOF mechanisms could be adopted for large number of various patients without expensive customized design for each individual. In the end, a gait rehab device design example is provided, and a prototype device driven by a constant speed motor is presented, which illustrates the feasibility of the proposed method.

Mechanical devices such as robots are widely adopted for limb rehabilitation. Due to the variety of human body parameters, the rehabilitation motion for different patients usually has its individual pattern; hence, we adopt clustering-based machine learning technique to find a limited number of motion patterns for upper-limb rehabilitation, so that they could represent the large amount of those from people who have various body parameters. By using the regression motion of the clustering result as the target, in this article, we seek to apply kinematic mapping-based motion synthesis framework to design a 1-degree-of-freedom (DOF) mechanism, such that it could lead the patients’ upper limb through the target motion. Also, considering rehab training generally involves a large amount of repetition on a daily basis, this article has developed a rehab system with unity3d based on virtual reality (VR). The proposed device and system could provide an immersive experience to the users, as well as the rehab motion data to the administrative staff for evaluation of users’ status. The construction of the integrated system and the experimental trial of the prototype are presented at the end of this article.