Kinematics and dynamics of a 4- P RUR Schönflies parallel manipulator by means of screw theory and the principle of virtual work

SummaryThis paper investigates the vibrations of hexarot simulators. The generalized modeling of kinematics and dynamics formulation of a hexarot mechanism is addressed. This model considers the flexible manipulator with the base motion. The dynamic formulation has been developed based on the principle of virtual work. The dynamic model consists of the stiffness of the different parts of the mechanism, the effects of gravity and inertia, torque and force related to the joints viscous friction. Finally, the response of the end effector at various frequencies has been presented, and the vibrations of the mechanism and the dynamic stability index have been investigated.

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Dynamic Modeling of Overconstrained Parallel Robot

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.373-375.34 ◽

2013 ◽

Vol 373-375 ◽

pp. 34-37

Author(s):

Jian Xin Yang ◽

Zhen Tao Liu ◽

Jian Wei Sun

Keyword(s):

Dynamic Modeling ◽

Virtual Work ◽

Parallel Robot ◽

Tree Structure ◽

Kinematics And Dynamics ◽

Dynamics Analysis ◽

Forward Dynamics ◽

Principle Of Virtual Work ◽

Closed Form Solutions ◽

Dynamics Models

The dynamic modeling method for parallel robot based on the principle of virtual work and equivalent tree structure is proposed by taking off the platform and the chains as well as degenerating parallel robot into a tree structure, the closed-form solutions for the inverse and forward dynamics models of parallel robot are derived. The method is applied on kinematics and dynamics analysis of a representative 3-RRR spherical parallel robot.

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Inverse dynamics modeling of a (3-UPU)+(3-UPS+S) serial-parallel manipulator

Robotica ◽

10.1017/s0263574714001817 ◽

2014 ◽

Vol 34 (3) ◽

pp. 687-702 ◽

Cited By ~ 5

Author(s):

Bo Hu ◽

Jingjing Yu ◽

Yi Lu

Keyword(s):

Parallel Manipulator ◽

Inverse Dynamics ◽

Virtual Work ◽

Principle Of Virtual Work ◽

Dynamics Modeling ◽

Dynamics Model ◽

Velocity Mapping

SUMMARYThe inverse dynamics model of a novel (3-UPU)+(3-UPS+S) serial–parallel manipulator (S-PM) formed by a 3-UPU PM and a 3-UPS+S PM connected in serial is studied in this paper. First, the inverse position, velocity, and acceleration of this S-PM are studied systematically. Second, the velocity mapping relations between each component and the terminal platform of (3-UPU)+(3-UPS+S) S-PM are derived. Third, the dynamics model of the whole (3-UPU)+(3-UPS+S) S-PM is established by means of the principle of virtual work. The process for establishing the dynamics model of this S-PM is fit for other S-PMs.

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Inverse Dynamics Formulation and Analysis of a Parallel Manipulator with 3DOFs Based on the Virtual Work Principle

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.455.360 ◽

2013 ◽

Vol 455 ◽

pp. 360-365

Author(s):

Yong Gang Li ◽

Li Xin Xu ◽

Hui Wang

Keyword(s):

Dynamic Optimization ◽

Parallel Manipulator ◽

Inverse Dynamics ◽

Virtual Work ◽

Hessian Matrix ◽

Parameters Estimation ◽

Principle Of Virtual Work ◽

Virtual Work Principle ◽

Optimization Control ◽

Strategy Design

Dynamics formulation is a primary task for dynamic optimization, control strategy design and servomotor parameters estimation of the parallel manipulator (PM). In this paper, by using the simple operation form of reciprocal screw and Lie Algebra, the compact expressions of complete Jacobian and Hessian matrix are derived. Then the inverse dynamics of 3PRS parallel manipulator is formulated based on the efficient principle of virtual work. In this model, the generalized forces of both actuation and constraint can be solved. Finally, a numerical simulation example is given to demonstrate this simple yet effective approach.

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Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work

Robotica ◽

10.1017/s0263574708004657 ◽

2009 ◽

Vol 27 (2) ◽

pp. 259-268 ◽

Cited By ~ 47

Author(s):

Yongjie Zhao ◽

Feng Gao

Keyword(s):

Parallel Manipulator ◽

Inverse Dynamics ◽

Virtual Work ◽

Equations Of Motion ◽

Principle Of Virtual Work ◽

Constraint Forces ◽

Dynamical Equations ◽

Robot System ◽

Lead Screw ◽

Moving Platform

SUMMARYIn this paper, the inverse dynamics of the 6-dof out-parallel manipulator is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. The dynamical equations of motion include the rotation inertia of motor–coupler–screw and the term caused by the external force and moment exerted at the moving platform. The approach described here leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure. Numerical simulation for the inverse dynamics of a 6-dof out-parallel manipulator is illustrated. The whole actuating torques and the torques caused by gravity, velocity, acceleration, moving platform, strut, carriage, and the rotation inertia of the lead screw, motor rotor and coupler have been computed.

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Inverse and forward dynamics of N-3RPS manipulator with lockable joints

Robotica ◽

10.1017/s0263574714002355 ◽

2015 ◽

Vol 34 (6) ◽

pp. 1383-1402 ◽

Cited By ~ 3

Author(s):

Ali Taherifar ◽

Hassan Salarieh ◽

Aria Alasty ◽

Mohammad Honarvar

Keyword(s):

Inverse Kinematics ◽

Parallel Manipulator ◽

Closed Loop ◽

Virtual Work ◽

Forward Dynamics ◽

Loop Structure ◽

Parallel Mechanisms ◽

Principle Of Virtual Work ◽

Kinematic Constraints ◽

Locking Mechanism

SUMMARYThe N-3 Revolute-Prismatic-Spherical (N-3RPS) manipulator is a kind of serial-parallel manipulator and has higher stiffness and accuracy compared with serial mechanisms, and a larger workspace compared with parallel mechanisms. The locking mechanism in each joint allows the manipulator to be controlled by only three wires. Modeling the dynamics of this manipulator presents an inherent complexity due to its closed-loop structure and kinematic constraints. In the first part of this paper, the inverse kinematics of the manipulator, which consists of position, velocity, and acceleration, is studied. In the second part, the inverse and forward dynamics of the manipulator is formulated based on the principle of virtual work and link Jacobian matrices. Finally, the numerical example is presented for some trajectories.

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Dynamic analysis of a 3-DOF 3-PUU parallel manipulator based on the principle of virtual work

2015 IEEE International Conference on Advanced Intelligent Mechatronics (AIM) ◽

10.1109/aim.2015.7222744 ◽

2015 ◽

Cited By ~ 4

Author(s):

Song Lu ◽

Yangmin Li

Keyword(s):

Dynamic Analysis ◽

Parallel Manipulator ◽

Virtual Work ◽

Principle Of Virtual Work

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Solving Inverse Kinematics and Driving Forces of a Novel 3RPS-3SPR Serial-Parallel Manipulator

Volume 7: 33rd Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2009-86175 ◽

2009 ◽

Author(s):

Bo Hu ◽

Yi Lu ◽

Jia Yin Xu ◽

Jing Jing Yu

Keyword(s):

Inverse Kinematics ◽

Parallel Manipulator ◽

Driving Forces ◽

Virtual Work ◽

Geometrical Constraint ◽

Principle Of Virtual Work ◽

Jacobian Matrices ◽

Numerical Example ◽

Dimension Constraint

The inverse kinematics and the driving forces of a 3RPS-3SPR serial-parallel manipulator (PM) with 6 degree of freedoms (DOFs) are solved in this paper. This 3RPS-3SPR serial-PM includes a lower 3-RPS PM and an upper 3-SPR PM. First, the inverse displacement is solved based on the geometrical constraint and the dimension constraint of this PM. Second, the 9×9 and 6×6 form inverse Jacobian matrices are derived and the driving forces are solved by using principle of virtual work. Finally, the numerical example is given.

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