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Jaime Gallardo-Alvarado,Mario A. García-Murillo,Md. Nazrul Islam,Mohammad H. Abedinnasab 대한기계학회 2017 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.31 No.10
This work deals with the inverse–forward kinematic analysis of a symmetric parallel manipulator equipped with a rotary actuator generator of three independent translations and one rotation motion. The closure equations of the displacement analysis are easily formulated based on the unknown coordinates of two points embedded in the moving platform. The input–output equations of velocity and acceleration of the robot are systematically obtained through the reciprocal-screw theory. The pseudo-kinematic pairs that connect the limbs to the fixed platform and a passive kinematic chain connected to the robot manipulator eliminate the handling of rank-deficient Jacobian matrices, which is an undisputable advantage from the computational point of view. Furthermore, this strategy allows the use of the Lie algebra se(3) without the inherent restrictions associated with the limited mobility of the robot.
A simple approach to solving the kinematics of the 4-UPS/PS (3R1T) parallel manipulator
Jaime Gallardo-Alvarado,Mario A. García-Murillo,Md. Nazrul Islam,Mohammad H. Abedinnasab 대한기계학회 2016 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.30 No.5
This work reports on the position, velocity and acceleration analyses of a four-degrees-of-freedom parallel manipulator, 4-DoF-PM for brevity, which generates Three-rotation-one-translation (3R1T) motion. Nearly closed-form solutions to solve the forward displacement analysis are easily obtained based on closure equations formulated upon linear combinations of the coordinates of three non-collinear points embedded in the moving platform. Then, the input-output equations of velocity and acceleration of the robot manipulator are systematically established by resorting to the theory of screws. To this end, the Klein form of the Lie algebra se(3) of the Euclidean group SE(3) is systematically applied to the velocity and reduced acceleration state in screw form of the moving platform cancelling the passive joint rates of the parallel manipulator. Numerical examples, which are confirmed by means of commercially available software, are provided to show the application of the method.
An application of screw theory to the kinematic analysis of a Delta-type robot
Jaime Gallardo-Alvarado,Albert L. Balmaceda-Santamaría,Eduardo Castillo-Castaneda 대한기계학회 2014 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.28 No.9
This paper reports on the kinematics of a translational parallel manipulator whose topology is close to the architecture of the famousDelta robot. The displacement analysis is presented in closed-form solution by applying a new strategy based on the unknown coordinatesof a point embedded to the moving platform. The input-output equations of velocity and acceleration of the robot are systematicallyobtained by resorting to reciprocal-screw theory. The singularities of the mechanism are explained through the input-output equation ofvelocity. Finally, a numerical example is provided to show the application of the method.
An approach to solving the forward kinematics of the 5-RPUR (3T2R) parallel manipulator
Jaime Gallardo-Alvarado,Mario A. Garcia-Murillo,Luis D. Aguilera-Camacho,Luis A. Alcaraz-Caracheo,X. Yamile Sandoval-Castro 대한기계학회 2023 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.37 No.3
This work is devoted to simplifying the formulation and solution of the closure equations associated with the forward kinematic problem (FKP) of the 5-RPUR parallel manipulator, a limited-DOF robot able to perform 3T2R motion. The analysis yields a set of eighteen nonlinear equations that are solved numerically through a combination of the homotopy continuation method and the usual Newton-Raphson technique. Unlike existing methods, the proposed approach is easy to follow and can be easily translated into computer codes. Numerical examples are provided with the aim to illustrate the potential and correctness of the proposed method.