Structural and Dimensional Synthesis of Overconstraint Symmetric 3T2R Parallel Robots Using Tait-Bryan-Angle Kinematic Constraints

Abstract

The basic parallel robotics principle of defining kinematic constraints as vector loops is transferred from the general 3T3R case to the 3T2R case by applying a nonlinear Tait-Bryan-angle rotation constraint using the intrinsic Z-Y -X convention. This presents an alternative way to the deduction of differential inverse kinematics by the theory of linear transformations. The resulting formulation is used in a permutational combined structural and dimensional synthesis. The modular approach allows to combine databases of serial and parallel robots without manual intervention. The validation shows the reproducibility of existing kinematic structures using the new kinematic formulation. The optimization scheme allows to obtain suitably dimensioned symmetric 3T2R parallel robots for a given task.

Mechatronic Device Control by Artificial Intelligence

“…Tait-Bryan angles were used to obtain the resulting rotation matrix while defining the orientation of the Ox2y2z2 coordinate system on the effector. The rotation method of this coordinate system is in the order Z1Y2X3, where indexes 1,2,3 symbolize the angles ψ, θ, ϕ, that were used for the rotation about each axis [21,22]. Tait-Bryan angles were used to obtain the resulting rotation matrix while defining the orientation of the Ox 2 y 2 z 2 coordinate system on the effector.…”

“…Tait-Bryan angles were used to obtain the resulting rotation matrix while defining the orientation of the Ox 2 y 2 z 2 coordinate system on the effector. The rotation method of this coordinate system is in the order Z 1 Y 2 X 3 , where indexes 1,2,3 symbolize the angles ψ, θ, φ, that were used for the rotation about each axis [21,22].…”