Seminar: New Ideation Techniques in Mechanism Design with Applications to Biomimetic and Rehabilitation Robotics

Abstract

A basic geometric fact useful to kinematic designers is that picking three points in space defines a circle.  A crank with length equal to the circle’s radius can be pinned at one end to the circle’s center so that its other end passes through the three points.  The next basic geometric fact is that a four-bar linkage, similar to the circle, can move a point on its coupler link through nine points in the plane.  Despite linkage design being an age old art and science, it was not until 1992 that it was discovered that a maximum of 8,652 four-bars exist for any nine points and the dimensions of these linkages were computed.  This sought-after result was enabled by the computational power of the day, and the creation of clever new algorithms for solving the largest polynomial systems.  Looking ahead, the size of these geometric questions continues to grow exponentially e.g. there should be far over a million six-bar linkages that pass through 15 points. However, today’s state-of-the-art solution techniques are limited in the size of the problems they can access.

In this seminar, I describe my approach for answering the next level of geometric questions, and how these results create software tools that greatly enhance the ideation phase of the mechanical design process.  The solution techniques used are based on polynomial homotopy continuation, with a new method proposed that avoids all computations that lead to roots at infinity.  Several examples are given of how theoretical results were transformed into software algorithms that lead to novel patentable devices.  Examples include biomimetic robot design, rehabilitative robotics, and automotive suspension design.

About the Speaker

Dr. Plecnik received his Ph.D. in mechanical engineering from the University of California, Irvine, in June 2015. His dissertation topic was on the computational kinematic design of mechanical linkages. He is currently a postdoc at the University of California, Berkeley where he received NSF EAGER funding on  Computational Kinematic Synthesis for Designing Millirobotic Systems.  His paper was awarded the 2015 A. T. Yang Memorial Award for the Best Paper in Theoretical Kinematics at the ASME International Design Engineering Technical Conferences.  While at UC Irvine, his research efforts lead to 3 provisional patent applications assigned to the Regents of California.

Dr. Plecnik’s research objective is to advance the ideation phase to regularly include non-intuitive, novel, and often patentable ideas that can only be discovered through computation. In order to advance the ideation of mechanical linkages, the mathematical toolset around solving large polynomial systems needs to advance as well, which he has identified as a current and future research direction. His work applies broadly to all fields that involve mechanical design including product design, robotics, and industrial machinery. In particular, insights from his current position have identified a need for mechanism ideation within robot locomotion. That is, although biologists have identified core principles of animal locomotion that are independent of size and morphology, the realm of minimally-actuated leg mechanisms consists of a short list of single-degree-of-freedom walking machines that were discovered by a few inventors. He wants to incorporate discovered principles of legged locomotion into kinematic synthesis theory.

Hosted by Professor Jami J. Shah