Design Challenges in the Development of Fast Pick-and-place Robots
The development of robotic systems has faced many challenges: First came what Freudenstein called “the Mount Everest” of kinematics. Thereafter came the challenge of finding all forwardkinematics solutions of a six-degree-of-freedom parallel robot. The tw
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Department of Mechanical Engineering & Centre for Intelligent Machines, McGill University, Montreal, QC, Canada Abstract The development of robotic systems has faced many challenges: First came what Freudenstein called “the Mount Everest” of kinematics. Thereafter came the challenge of finding all forwardkinematics solutions of a six-degree-of-freedom parallel robot. The two foregoing problems are largely solved by now. The new challenge is the development of ever faster pick-and-place four-degree-offreedom robots. The limit of the serial version thereof was reached in the late nineties, with a record speed of two cycles per second. This called for the development of parallel versions of the same. Some industrial robots of this kind, carrying three to four limbs, are out in the market. With the purpose of simplifying their morphology and reducing their footprint, two-limb robots have started emerging. The challenge here is the transmission of force and motion from the two actuators of each limb, mounted on a common base, to produce two independent motions, normally pan and tilt. Discussed in this paper are the theoretical and practical hurdles that the robot designer faces in this quest.
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Introduction
The early robots, namely, Unimate (Westerlund, 2000) and the Stanford Arm, had a simple architecture, intended to ease the transformation from Cartesian to joint coordinates and vice versa, which led their designers to provide them with one prismatic joint. The need for robots with a more dextrous architecture, which required six revolute joints, brought about the challenge of the inverse kinematics of a serial robot supplied with six revolute joints, but otherwise of arbitrary architecture. This problem is equivalent to that of finding the input-output function of the closed seven-revolute linkage, which Freudenstein dubbed “the Mount Everest of kinematics.” Using different elimination procedures, Li (1990), Li et al. (1991) and Raghavan and Roth (1990), devised independent algorithms for the computation V. Padois, P. Bidaud, O. Khatib (Eds.), Romansy 19 – Robot Design, Dynamics and Control, CISM International Centre for Mechanical Sciences, DOI 10.1007/978-3-7091-1379-0_8, © CISM, Udine 2013
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of the coefficients of the 16th-degree univariate polynomial that had been anticipated by Primrose (1986). Once Freudentstein’s Mount Everest problem was under control, researchers turned their attention to the next challenge, namely, the derivation of the minimal univariate polynomial that would yield all the forward kinematics solutions of the general Stewart-Gough platform (SGP). This is a six-degree-of freedom parallel robot with two platforms coupled by six limbs, of arbitrary architecture. Independently, Wampler (1996) and Husty (1996) devised procedures to derive this polynomial, although Wampler did not pursue the univariate polynomial approach and preferred to cast the problem in a form suitable for its solution by means of polynomial continuation. Husty did derive the 40th-degree univariate polyn
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