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Special GRASP Seminar: Zexiang Li, Hong Kong University of Science and Technology, “From Da Vinci to Five-Axes Machines”

April 9, 2013 @ 3:30 pm - 4:30 pm

Abstract: A five-axes machine is capable of rotating its tool spindle in a high
angle, and therefore largely increases efficiency by machining multiple
faces of a workpiece with only one setup. The rotation motion type of
five-axes machining is a two dimensional submanifold of the special
Orthogonal group SO(3). For decades, the Hooke joint model is taken for
granted to describe such a motion type. However, the Hooke joint model
has a topology of a torus, which contradicts the fact that the spindle
rotation has a topology of a sphere. The Hooke joint model is not an
ideal model to type synthesize parallel kinematics machine with
omni-directional high angle capability. Inspired by a recent survey
study, we discovered that there exists a unified model for the motion
types ranging from kinesiology of Da Vinci and Listing?s law of eye
movement to Rzeppa?s constant velocity joint, Zlatanov?s multi-mode
parallel mechanism and five-axes machining. This newly discovered model,
known as an ?exponential submanifold?, has the correct sphere topology
and successfully explains the inconsistency of the Hooke joint model. It
is shown that exponential submanifold has its unique topological and
geometrical properties, which naturally leads to an omni-directional
high angle capability. Therefore, exponential submanifold is not only
the correct kinematics model for five-axes machines, rehabilitation
robotics, eye movement, constant velocity joints etc., but also an
indispensable mathematics tool for type synthesis.


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Zexiang Li attended the South-Central University in 1978, received his
BS (with honor) degrees in Electrical Engineering and Economics from
Carnegie-Mellon University in 1983, his MS degree in EECS in 1985, MA in
mathematics and PhD in EECS in 1989, all from the University of
California at Berkeley. He worked at ALCOA, the Robotics Institute of
CMU and the AI Lab of MIT (89-90). He was an assistantprofessor at the
Courant Institute of New York University (90-92). In 1992, he joined the
Department of Electronic and Computer Engineering of the Hong Kong
University of Science and Technology and is currently a professor of the
department. He founded the Automation Technology Center (ATC) and
currently serves as its director.

Zexiang Li received the ALCOA Foundation Fellowship in 1979, and the
E. Anthony Fellowship in 1983. He was a recipient of the University
Scholar award from CMU in 1983, the E.I. Jury award from UC Berkeley in
1989, the Research Initiation award from NSF (US) in 1990, the
Outstanding Young Researcher award (Class B) from NSF China in 2000, the
LEAD award from AMI, USA in 2001, and the Natural Science award (3rd
class) from China in 1997. He became an IEEE Fellow in 2008.

Zexiang Li served as a panel member of the Hong Kong Research Grants
Council (RGC), an overseas member of the Natural Science Foundation of
China (NSFC), and an associate editor for the IEEE Trans. on Robotics
and Automation. He was the general Chair for the 2011 IEEE International
Conference on Robotics and Automation (ICRA).

Zexiang Li’s research areas of interests include multifingered
robotic hand, parallel manipulators, workpiece localization and
inspection, motion control, precision assembly, and unmanned aerial
vehicles (UAVs). He is the author of more than 100 journal and
conference papers, and the books A Mathematical Introduction to Robotic
Manipulation (CRC Press 1993), and Nonholonomic Motion Planning (Kluwer

Zexiang Li cofounded several companies with his colleagues and
students from the Automation Technology Center, including Googol
Technology, the first motion control company in China, iFlight
Technology (or Dajian In- novation), a leading company in UAV products,
Parallex, a company specializing in LED and IC packaging automation
equipment, and Lie Group Automation.


April 9, 2013
3:30 pm - 4:30 pm
Event Category: