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UID:20260513T155102EDT-5569Vn6mxV@132.216.98.100
DTSTAMP:20260513T195102Z
DESCRIPTION:\n	CIM Seminar in Robotic Mechanical Systems \n\n\n \n\n\n	Speake
 r: Prof. Manfred L. Husty\n\n	University of Innsbruck\, \n\n	Austria\n\n	 \n
 \n	\n		Abstract: A planar parallel 3-RPR parallel manipulator consists of thr
 ee anchor points (A\;B\;C) in a base connected via three extensible legs (
 r1\; r2\; r3) to a triangular platform (D\;E\; F). In the direct kinematic
 s (DK) one has to compute the pose of the platform when the design of the 
 manipulator (location of the base points and the shape of the moving platf
 orm) and the lengths of the legs are given. It is well known that this tas
 k allows six solutions. When some of the solutions of the DK coincide the 
 manipulator becomes singular. In the presentation\, it will be shown that 
 multiple solutions of the direct kinematics are a new way of looking into 
 the notions of 'shakiness' of mechanisms or 'flexibility' of pin jointed f
 rameworks of rigid bars. For the first time general conditions for maximal
  (= 6) coinciding solutions will be given. It will be discussed that multi
 ple solutions of the DK are far beyond the classical singularity theory of
  a manipulator. They belong to so called constraint singularities which de
 scribe special situations in the configuration space of the manipulator.\n
 \n		The discussion is done within the framework of algebraic geometry and po
 lynomial equations\, because multiple solutions are closed sets. We have t
 herefore also to explain the advantages and limitations of this approach.
 \n\n		 \n	\n\n	Bio:\n\n	Prof. Dr. Dr.(hc) Manfred Husty is Emeritus Professor f
 rom University of Innsbruck\, Austria. His research\n		milestones in kinemat
 ic geometry are a) closed form solution to the direct kinematics of a gene
 ral six\n		legged Stewart-Gough parallel manipulator which was until 1994 th
 e most challenging unsolved problem in\n		robotic kinematics and b) closed f
 orm solution of inverse kinematics of a general 6R serial robot using\n		kin
 ematic mapping in 2005 which greatly simplifies and accelerates computatio
 n. This makes it more effective\n		as a real time procedure than earlier res
 ults modelled in Euclidean space.\n\n	 \n\n
DTSTART:20230525T200000Z
DTEND:20230525T210000Z
LOCATION:Zames Seminar Room\, MC 437\, McConnell Engineering Building\, CA\
 , QC\, Montreal\, H3A 0E9\, 3480 rue University
SUMMARY:Multiple Solutions of Direct Kinematics of 3-RPR Parallel Manipulat
 ors
URL:https://www.mcgill.ca/cim/channels/event/multiple-solutions-direct-kine
 matics-3-rpr-parallel-manipulators-351720
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