Robotic mechanisms in general can be of either serial-chain, parallel-chain, or hybrid (a combination of both parallel and serial chains) geometry. While it can be asserted that kinematic theories and techniques are well established for fully serial-chain manipulators, the same assertion cannot be made when it is considered in the general context. In this article, we present a general procedure for systematic formulation and characterization of the instantaneous kinematics for a robotic mechanism with a general parallel-chain geometry. A kinestatic approach based on screw system theory is adopted in this treatment. The resulting equation is a compact Jacobian matrix of the system which includes attributes from not only the active joints but also the passive constraints. An example has been provided to demonstrate the methodology as well as its theoretical feasibility.

Issue Section:
Research Papers
Topics:
Manipulators, Chain, Geometry, Kinematics, Robotics, Jacobian matrices, Screws, Systems theory
1.
Behi
F.
,
1988
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2.
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,”
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,”
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,
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On the Numerical Kinematic Analysis of General Parallel Robotic Manipulators
,”
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,”
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The Elliptic Polarity of Screws
,”
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,”
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Duffy
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The Fallacy of Modern Hybrid Control Theory That is Based on Orthogonal Complements of Twist and Wrench Spaces
,”
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16.
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17.
Lipkin
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, and
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,
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Hybrid Twist and Wrench Control for a Robotic Manipulator
,”
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.
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