Journal of Mechanisms and Robotics-Transactions of the Asme最新文献

Convex combination of points is a fundamental operation in computational geometry. By considering rigid-body displacements as points in the image spaces of planar quaternions, quaternions and dual quaternions, respectively, the notion of convexity in Euclidean three-space has been extended to kinematic convexity in $SE\left(2\right),SO\left(3\right)$ , and $SE\left(3\right)$ in the context of computational kinematic geometry. This paper deals with computational kinematic geometry of bounded planar objects rather than that of infinitely large moving spaces. In this paper, we present a new formulation for kinematic convexity based on an average-distance minimizing motion sweep of a bounded planar object. The resulting 1-DOF motion sweep between two planar poses is represented as a convex combination in the configuration space defined by $(x,y,z)$ where $(x,y)$ is associated with the location of the centroid of the planar object and $z=\text{sin}\theta$ with $\theta$ being the angle of rotation. For three poses, a 2-DOF motion sweep is developed that not only minimizes the combined average squared distances but also attains a convex-combination representation so that existing algorithms for convex hull of points can be readily applied to the construction and analysis of kinematic convex hulls. This results in a new type of convex hull for planar kinematics such that its boundaries are defined by the average-distance minimizing sweeps of the bounded planar object.

This article presents an exploratory study of a new family of parallel mechanisms with multiscale (micro/macro) motion capabilities. These composite serial-in-parallel mechanisms use kinematic redundancy and two sets of macro and micro actuators to achieve multiscale motion. Use of twisted wire actuators (TWAs) is considered as a low-cost alternative for achieving micromotion. A kinematically redundant 3RRPR planar parallel robot is used as a case study for task-based design of these robots with considerations of macro and micromotion workspace, dexterity, minimal motion resolution, and end-effector error considering the use of low-cost TWAs for achieving micromotion. Task-based considerations for the microworkspace are used to illustrate the effect of the TWAs on the micromotion kinematics. An experimental study shows that, because of the use of TWAs, it is possible to achieve motion resolutions on the order of a few micrometers despite using low-cost manufacturing techniques and actuators. The use of TWAs is shown to also significantly alter the kinematic characteristics of the robot at the microscale. The modeling framework of this article can guide designers in key design considerations for parallel robots with multiscale motion capabilities. Results of this article can be used to guide users in the selection of TWAs and in determining the threshold when the robot should switch from macro to micromotion and to facilitate a smooth transition via redundancy resolution.

Understanding legged locomotion in various environments is valuable for many fields, including robotics, biomechanics, rehabilitation, and motor control. Specifically, investigating legged locomotion in compliant terrains has recently been gaining interest for the robust control of legged robots over natural environments. At the same time, the importance of ground compliance has also been highlighted in poststroke gait rehabilitation. Currently, there are not many ways to investigate walking surfaces of varying stiffness. This article introduces the variable stiffness treadmill (VST) 2, an improvement of the first version of the VST, which was the first treadmill able to vary belt stiffness. In contrast to the VST 1, the device presented in this paper (VST 2) can reduce the stiffness of both belts independently, by generating vertical deflection instead of angular, while increasing the walking surface area from 0.20 m² to 0.74 m². In addition, both treadmill belts are now driven independently, while high-spatial-resolution force sensors under each belt allow for measurement of ground reaction forces and center of pressure. Through validation experiments, the VST 2 displays high accuracy and precision. The VST 2 has a stiffness range of 13 kN/m to 1.5MN/m, error of less than 1%, and standard deviations of less than 2.2 kN/m, demonstrating its ability to simulate low-stiffness environments reliably. The VST 2 constitutes a drastic improvement of the VST platform, a one-of-its-kind system that can improve our understanding of human and robotic gait while creating new avenues of research on biped locomotion, athletic training, and rehabilitation of gait after injury or disease.

This paper studies the statistical concept of confidence region for a set of uncertain planar displacements with a certain level of confidence or probabilities. Three different representations of planar displacements are compared in this context and it is shown that the most commonly used representation based on the coordinates of the moving frame is the least effective. The other two methods, namely the exponential coordinates and planar quaternions, are equally effective in capturing the group structure of SE(2). However, the former relies on the exponential map to parameterize an element of SE(2), while the latter uses a quadratic map, which is often more advantageous computationally. This paper focus on the use of planar quaternions to develop a method for computing the confidence region for a given set of uncertain planar displacements. Principal component analysis (PCA) is another tool used in our study to capture the dominant direction of movements. To demonstrate the effectiveness of our approach, we compare it to an existing method called rotational and translational confidence limit (RTCL). Our examples show that the planar quaternion formulation leads to a swept volume that is more compact and more effective than the RTCL method, especially in cases when off-axis rotation is present.