Search

• A new overconstrained 2R1T parallel manipulator with fixed actuators. • Only 13 single-DOF joints, simple inverse kinematics and few singularities. • Great performances in the levels of kinematics, stiffness and dynamics. • Suitable parallel module of five-axis hybrid machines through machining experiment. • Addition and multiplication in the geometric algebra avoid complex calculations. Five-axis hybrid machine tools are important equipment for highly efficient precision machining of complex workpieces, in which a key part is parallel manipulators (PMs) with two rotations and one translation (2R1T). In view of many single-degree-of-freedom (DOF) joints and virtual output rotational axes in most existing 2R1T PMs, a new 2R1T 2PRU-PSR PM with two certain rotational axes is proposed, which is composed of 13 single-DOF joints and only one S joint and is fully actuated with stationary actuators. Using geometric algebra as a mathematical tool, the mobility and kinematic performance evaluation considering the motion/force transmissibility are presented. With the motion/force transmissibility taken as the optimal index, the dimensional parameters of the 2PRU-PSR PM are optimized to obtain an improved transmission workspace without singular configurations. Based on the optimized parameters, stiffness and dynamic analyses of the 2PRU-PSR PM are presented in the framework of geometric algebra. The results reveal that the 2PRU-PSR PM exhibits excellent performance in the levels of kinematics, stiffness, and dynamics. Finally, a five-axis hybrid prototype is built based on the optimized 2PRU-PSR PM and two serial guides. Machining experiments show that the 2PRU-PSR PM is suitable as a parallel module for five-axis hybrid machines. [ABSTRACT FROM AUTHOR]

This work addresses the inverse kinematics of serial robots using conformal geometric algebra. Classical approaches include either the use of homogeneous matrices, which entails high computational cost and execution time, or the development of particular geometric strategies that cannot be generalized to arbitrary serial robots. In this work, we present a compact, elegant and intuitive formulation of robot kinematics based on conformal geometric algebra that provides a suitable framework for the closed-form resolution of the inverse kinematic problem for manipulators with a spherical wrist. For serial robots of this kind, the inverse kinematics problem can be split in two subproblems: the position and orientation problems. The latter is solved by appropriately splitting the rotor that defines the target orientation in three simpler rotors, while the former is solved by developing a geometric strategy for each combination of prismatic and revolute joints that forms the position part of the robot. Finally, the inverse kinematics of 7 DoF redundant manipulators with a spherical wrist is solved by extending the geometric solutions obtained in the non-redundant case. • The IK of serial robots with a spherical wrist is solved in closed-form. • The position problem is solved by the manipulation of different geometric entities. • The orientation problem is solved by the algebraic manipulation of a rotor. • The developed method is extended to 7 DoF serial robots with a spherical wrist. [ABSTRACT FROM AUTHOR]