Kinematic and dynamic analysis of a serial manipulator with local closed loop mechanisms

Abstract

This paper addresses the kinematic and dynamic modelling and analysis for a robot arm consisting of two hydraulic cylinders driving two revolute joints of the arm. The two cylinders and relevant links of the robot constitute two local closed kinematic chains added to the main robot mechanism. Therefore, the number of generalized coordinates of the mechanical system is increased, and the mathematical modelling is more complex that requires a formulation of constraint equations with respect to the local closed chains. By using the Lagrangian formulation with Lagrangian Multipliers, the dynamic equations are first derived with respect to all extended generalized coordinates. Then a compact form of the dynamic equations is yielded by canceling the Multipliers. Since the obtained dynamic equations are expressed in terms of independent generalized coordinates which are selected according to active joint variables of the arm, the equations could be best suitable for control law design and implementation. The simulation of the forward and inverse kinematics and dynamics of the arm demonstrates the motion behavior of the robot system.

Velocity and Singularity Analysis of a 5-DOF (3T2R) Parallel-Serial (Hybrid) Manipulator

“…Expression (16) represents a system of three linear equations with respect to unknown components of 𝛚. In addition, 3 × 3 skew-symmetric matrices have rank two [33] (p. 22); therefore, we cannot use (16) to find unique 𝛚 . To obtain the third independent equation, we can equate the last rows of both sides of (15), concerning (9):…”

“…Many researchers have studied the kinematics of the hybrid robots, including their position and velocity analysis. For example, these issues were considered by Tanev [7] for two serially connected tripod mechanisms; Moosavian et al [8] for a planar robot with a serial PUMA-type robotic arm attached to its output link; Zheng et al [9] for two tripods, designed such that the smaller one is inside the larger one; Nazari et al [10] for a tripod with cylindrical and revolute joints and a serial robotic arm mounted on the tripod moving plate; Kucuk and Gungor [11] for a Stewart platform placed on a SCARA-type robot; Zhang et al [12] for a 5-DOF Exechon robot, which consists of a tripod and a 2-DOF serial wrist mechanism; Xu et al [13] for a polishing machine based on a translational Delta-like robot with linear drives and a separate serial module with three rotational DOFs; Gim et al [14] for a humanoid robotic leg composed of two planar closed loops, each followed by a link with passive joints and connected to each other and the moving plate through an actuated revolute joint; Milutinović et al [15] for a Tricept robot based on a tripod with translational DOFs equipped with a 2-DOF wrist; My and Hoan [16] for a serial robotic arm with two intermediate parallel loops.…”

Differential equations of motion in matrix form of multibody systems driven by electric motors

“…Modelling and simulation of an MBS has attracted numerous researchers. Many works deal with modelling of MBS [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. There are some approaches proposed in literature to formulate dynamic equations of an MBS including Newton-Euler equations, Lagrangian formulation, principle of virtual work, Jourdain principle, and Kane equation [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Optimal Design for Robot Arm to Lift Electrical Cabinets with a Mass of 150 Kg

“…Two variables of the algorithm have been proposed; one method uses iterations to find a solution based on in-depth collision analysis, and the second method uses the PSO algorithm. The article [5] deals with the modeling and analysis of kinematics and kinematics for a robot arm consisting of two hydraulic cylinders that drive two rotating joints of the arm. The two cylinders and associated links of the robot form two locally closed kinematic chains that are added to the main robot mechanism.…”