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

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.

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

Robotica ◽  
2015 ◽  
Vol 34 (6) ◽  
pp. 1383-1402 ◽  
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.

A Unified Approach to Solving Driving Forces in Spatial Parallel Manipulators With Less Than Six DOFs

2006 ◽  
Vol 129 (11) ◽  
pp. 1153-1160 ◽  
Author(s):  
Yi Lu ◽  
Bo Hu
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Driving Forces ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Unified Approach ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Constrained Equations ◽  
Serial Mechanism

A unified approach to solving driving forces in spatial parallel manipulators with less than six DOFs is proposed. First, the geometric constrained equations of the parallel manipulators are derived, and some independent pose parameters and a common transformation matrix with three translations and three Euler rotations are determined. Second, the common formulas for solving inverse kinematics, the Jacobian matrix, and velocity are derived. Third, a common virtual serial mechanism with three virtual prismatic joints and three virtual revolute joints corresponding to three Euler rotations is constructed. Fourth, a common analytic formula for solving driving forces in spatial parallel manipulators with less than six DOFs is derived by using the principle of virtual work and the virtual serial mechanism. Finally, a 3-SPR parallel manipulator with three DOFs and a 4SPS+SPR parallel manipulator with five DOFs are presented to illustrate the use of the unified approach to solve their inverse kinematics and the driving forces. The solving results are verified by the simulation mechanisms.

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

Robotica ◽  
2014 ◽  
Vol 34 (3) ◽  
pp. 687-702 ◽  
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.

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

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.

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

Robotica ◽  
2009 ◽  
Vol 27 (2) ◽  
pp. 259-268 ◽  
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.

Solving active wrench of limited-degree of freedom parallel manipulators based on translational/rotational Jacobian matrices

2009 ◽  
Vol 223 (3) ◽  
pp. 221-229 ◽  
Author(s):  
Y Lu ◽  
B Hu ◽  
J Yu
Keyword(s):  
Virtual Work ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Principle Of Virtual Work ◽  
Jacobian Matrices ◽  
Limited Degree

A methodology is proposed for unified solving active wrench of the limited-degree of freedom (DOF) parallel manipulators (PMs). First, the geometric constraints and the inverse displacement kinematics are analysed. Second, the formulae for unified solving the inverse/forward velocity and the translational/rotational Jacobian matrices and inverse/forward Jacobian matrices are derived. Third, the analytic formulae for unified solving the active wrench of limited-DOF PMs are derived based on the principle of virtual work. Finally, a 3-DOF PM with linear/rotational active legs is presented to illustrate the use of the methodology.

Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work

1999 ◽  
Vol 122 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Computational Algorithm ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Principle Of Virtual Work ◽  
Dynamical Equations ◽  
Jacobian Matrices ◽  
Systematic Methodology ◽  
Moving Platform

This paper presents a systematic methodology for solving the inverse dynamics of a Stewart-Gough manipulator. Based on the principle of virtual work and the concept of link Jacobian matrices, a methodology for deriving the dynamical equations of motion is developed. It is shown that the dynamics of the manipulator can be reduced to solving a system of six linear equations in six unknowns. A computational algorithm for solving the inverse dynamics of the manipulator is developed and several trajectories of the moving platform are simulated. [S1050-0472(00)00401-3]

Inverse Dynamics of a 6-DOF Decoupling Manipulator

2014 ◽  
Author(s):  
Taoran Liu ◽  
Feng Gao ◽  
Xianchao Zhao ◽  
Chenkun Qi
Keyword(s):  
Inverse Kinematics ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Principle Of Virtual Work ◽  
Real Time Control ◽  
Model Accuracy ◽  
Lower Weight ◽  
Time Control ◽  
Speed Reducer ◽  
Forward And Inverse Kinematics

In this paper, the kinematics and inverse dynamics of a 6-dof full decoupling parallel manipulator is presented. The forward and inverse kinematics solution can be easily obtained and simplify the real-time control due to 6 dof motion full decoupling. Three motors are embedded into the moving platform to realize rotational motion, simple kinematics and isotropic configurations due to the motors and speed reducers have a lower weight. An effective inverse dynamics of the manipulator is derived by the principle of virtual work. The existence of speed reducer for motors have advantages of decreasing mechanical couplings between axes and the full varying inertias are not directly onto each motor output shaft. Since the presence of speed reducer and in order to improve dynamic model accuracy, the inertia of motor rotor-reducer should be computed. Finally, numerical simulation of the inverse dynamics provides that the actuating torques created by gravity, velocity, acceleration and decoupling torque, coupling torque have been computed.

Sign in / Sign up

Export Citation Format

Share Document