Abstract
The paper proposes a mathematical method for redefining motion parameterizations based on the joint-space representation of parallel robots. The study parameters of SE(3) are used to describe the robot kinematic chains, but, rather than directly analyzing the mobile platform motion, the joint-space of the mechanism is studied by eliminating the Study parameters. From the loop equations of the joint-space characterization, new parameterizations are defined, which enable the placement of a mobile frame on any mechanical element within the parallel robot. A case study is presented for a medical parallel robotic system in which the joint-space characterization is achieved and based on a new defined parameterization, the kinematics for displacement, velocities, and accelerations are studied. A numerical simulation is presented for the derived kinematic models, showing how the medical robot guides the medical tool (ultrasound probe) on an imposed trajectory.
Highlights
One fundamental problem in robotics refers to mechanism analysis and synthesis, which, in general, provides mathematical information regarding: (i) the laws of motion of the mechanical system; (ii) the singular configurations of the robot; and, (iii) the robot workspace.There are various mathematical methods used for mechanism analysis and synthesis, with two categories being prominent, namely the vector methods and the algebraic methods
The main goal of the paper is to show how a specific motion parameterization method, which describes the joint-space of a parallel robot, may be used in achieving other parameterizations and how the newly defined parameterizations may be used in kinematic studies
1 = 45°]; the 1entry point is defined as a Remote Center of Motion (RCM) point; the entry point is defined as a Remote
Summary
There are various mathematical methods used for mechanism analysis and synthesis, with two categories being prominent, namely the vector methods and the algebraic methods. Examples for vector methods are: the Denavit-Hartenberg convention (based on homogeneous matrix representation of SE(3)), used especially for serial mechanical chains [1], with a novel algorithm for automatic identification proposed in [2]; screw theory, which may be used even for error analysis in parallel mechanisms [3] or calibration of parallel mechanism [4]; and, Euler parameters used in the study of spherical displacement [5,6]. The study parameters method has the advantage that it describes the global kinematics
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