Dexterity distribution design for attitude adjustment of multi-joint robotics based on singularity-free workspace decomposition

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Abstract
This paper presents a dexterity distribution design method for attitude adjustment of multi-joint robotics based on singularity-free workspace decomposition (SWD). The requirement of attitude adjustment for platform is described by time-varying Euler angles, by which the structural prototyping of universal-prismatic-spherical + spherical (UPS + S) parallel robot body can be generated via mechanism concept design. According to Kutzbach-Grubler formula regarding degree of freedom (DOF), the forward kinematics model is built, meanwhile, the reachable posture workspace of the robot can be depicted in 3D space by exploiting tilt-and-torsion method. The Jacobian matrix is extracted to reckon dexterous performance of the mechanism, including condition number, minimum singular value, manipulability and comprehensive evaluation index. The singularity degree within the design domain, from singularity-free to fully singularity, is comparatively ranked in polar coordinates, which constitutes the essence of SWD, the performance spectrum corresponding to the structural parameters can hereby be acquired for larger workspace and smaller singularity. The impedance control errors with parameter perturbation further validate the consistency of the singularity-free attitude from the perspective of dynamics. The physical experiments are carried out to verify the outcomes by virtue of multi-axis pose sensor array. Hence the presented SWD method has important application prospects regarding DOF coupling, especially in medical rehabilitation, industrial robotics, aerospace manufacturing and so forth.

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