Session: Research Posters

Paper Number: 112685

112685 - Interactive Visualization Tools for the Study of Spherical and Spatial Kinematics 

This article presents pedagogy, and associated visualization software, for the study of spatial and spherical triangles. In addition, associated student learning activities that utilize the interactive visualization tools, as well as rapid prototyping with additive manufacturing techniques are presented.

Spatial and spherical triangles serve as the geometric foundation for spatial and spherical mechanism design; both synthesis and analysis. Moreover, the conceptualization and visualization of triangles facilitates the mastery of the synthesis and analysis of spatial and spherical mechanisms. The interactive visualization software tools have been developed to facilitate the teaching and learning of spatial and spherical mechanisms at the graduate and undergraduate levels. The trigonometry employed is briefly reviewed. Next, the interactive visualization software tools are summarized. Finally, pedagogical tools including lesson plans, in-class activities, and student group projects for active and project-based learning are presented.

Spatial triangles are defined by three skew lines in three-dimensional space. The sides of the triangle may be visualized by rendering a line segment along the common normal of the associated vertex pair; from one vertex to the other. Spatial triangles are often encountered in the studies of spatial kinematics, kinematic analysis of spatial mechanisms, and the synthesis of spatial mechanisms. Most frequently, one’s first encounter with spatial triangles occurs in the study of the position analysis of spatial mechanisms. As an example, the complete position analysis of the spatial 4C mechanism can be accomplished by determining the interior angles and sides of the spatial triangles associated with the mechanism’s spatial quadrilateral. Additional examples of encountering spatial triangles including spatial screw triangles; opposite screw quadrilaterals; spatial CC, CR, and RC dyad triangles; and the like.

Spherical triangles are defined by three great circles where each great circle is the intersection of the sphere with a plane passing through the center of the sphere. There are six points on the surface of the sphere determined by the intersections of these great circles. These intersections define the vertices of a spherical triangle. As an example of the application of spherical triangles, consider the position analysis of the spherical four-bar mechanism. Determining the interior angles and sides of the mechanism’s associated spherical triangles yields its complete position analysis. Additional examples of encountering spherical triangles include spherical pole triangles and spherical dyad triangles,

It is hoped that the dissemination of these pedagogical tools, and the associated interactive visualization software, will facilitate the learning and advancement of spatial and spherical kinematics and mechanism design techniques at both the graduate, and undergraduate, levels.

 

Presenting Author: Pierre Larochelle South Dakota School of Mines & Technology

Presenting Author Biography: Pierre Larochelle serves as Department Head and Professor of Mechanical Engineering at the South Dakota School of Mines & Technology. Previously, he served as an Associate Dean and Professor of Mechanical Engineering at the Florida Institute of Technology. His research focuses on the design of complex robotic mechanical systems and enabling creativity and innovation in design. He is the founding director of the RObotics and Computational Kinematics INnovation (ROCKIN) Laboratory, has over 100 publications, holds three US patents, and serves as a consultant on robotics, automation, machine design, creativity & innovation, and computer-aided design. In 2012, at NASA’s request, he created a 3-day short course on Creativity & Innovation. This course has been very well received, and he has taught it exclusively more than 30 times at NASA’s various centers and laboratories across the nation to more than 600 of NASA’s scientists and engineers. He currently serves as the Chair of the U.S. Committee on the Theory of Mechanisms & Machine Science and represents the U.S. in the International Federation for the Promotion of Mechanism & Machine Science (IFToMM) (2016-22). He serves as a founding Associate Editor for the ASME Journal of Autonomous Vehicles and Systems (2020-23). Moreover, he serves on the Executive Committees of ASME’s Department Heads Committee and of ABET’s Engineering Accreditation Commission (EAC). He serves as an ABET Accreditation Visit Team Chair. He has served as Chair of the ASME Design Engineering Division (2018-2019) and the ASME Mechanisms & Robotics Committee (2010-2014), and as an Associate Editor for the ASME Journal of Mechanisms & Robotics (2013-19), the ASME Journal of Mechanical Design (2005-11), and for Mechanics Based Design of Structures & Machines (2006-13). He is a Fellow of the American Society of Mechanical Engineers (ASME), a Senior Member of IEEE, and a member of Tau Beta Pi, Pi Tau Sigma, ASEE, and the Order of the Engineer.

Authors:

Pierre Larochelle South Dakota School of Mines & Technology