The subject of this paper is a special class of closedchain manipulators. First, we analyze a family of twodegree-of-freedom (dof) five-bar planar linkages. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the “inverse kinematics” and the “direct kinematics” matrices. It is shown that the loci of points of the wo...

In a recent paper, Andrews, Dixit, and Yee introduced a new spt-type function spt ω (n), which is closely related to Ramanujan’s third order mock theta function ω(q). Garvan and Jennings-Shaffer introduce a crank function which explains congruences for spt ω (n). In this note, we study asymptotic behavior of this crank function and confirm a positivity conjecture of the crank asymptotically. We...

The results of this thesis concern folding of one-dimensional objects in two dimensions: planar linkages. More precisely, a planar linkage consists of a collection of rigid bars (line segments) connected at their endpoints. Foldings of such a linkage must preserve the connections at endpoints, preserve the bar lengths, and (in our context) prevent bars from crossing. The main result of this the...

Two degree-of-freedom (2-DOF) closed spatial linkages can be useful in the design of robotic devices for spatial rigid-body guidance or manipulation. One of the simplest linkages of this type, without any passive DOF on its links, is the revolutespherical-revolute-spherical (RSRS) four-bar spatial linkage. Although the RSRS topology has been used in some robotics applications, the kinematics st...

This paper presents a methodology to enhance an interactive simulation system using Augmented Reality (AR) in the field of teaching/learning dynamics. The 3D-simulation model is being developed as a first step in order to develop an interactive (AR) book for engineering students. The purpose is to illustrate the benefits of enhancing the computer-aided simulation (CAS) using augmented reality t...

We show how four-bar linkages can be designed using non-convex optimization techniques. Our generative design software takes as input a curve that needs to be reproduced by a four-bar linkage and outputs the best assembly that approximates this curve. We model the problem using quadratic constraints and show how redundant constraints help to solve the problem. We also provide an algorithm that ...

Augmented reality (AR) is a technology that enables the users to visualize and interact with 3D virtual object, which is digitally processed and augmented in real time and environments. The use of AR in education has a wide potential of providing learners with a new type of learning material, and it has the capability to enrich the learning experience; especially in learning the kinesthetic and...