Dynamic Modeling of Parallel Manipulators

1996 ◽  
Author(s):  
Ivan J. Baiges ◽  
Joseph Duffy
Keyword(s):  
Dynamic Response ◽  
Parallel Manipulator ◽  
Coupling Effect ◽  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Inverse Dynamic ◽  
Inverse Dynamic Analysis ◽  
High Degree ◽  
Degree Of Coupling ◽  
Explicit Equations Of Motion

Abstract The dynamic response is an important consideration when designing and controlling manipulators. This dynamic response can be better understood with the explicit equations of motion. This paper presents the derivation of the explicit equations of motion for a parallel manipulator using Kane’s Method. These equations illustrate the high degree of coupling existing in this type of manipulator. A simulation program is developed with the equations of motion and used for the inverse dynamic analysis of the system. The results of the tests indicate that the most important coupling effect is caused by gravity.

Computation of the Output Torque, Power and Work of the Driving Motor for a Redundant Parallel Manipulator

2013 ◽  
pp. 76-91
Author(s):  
Yongjie Zhao
Keyword(s):  
External Force ◽  
Parallel Manipulator ◽  
Numerical Integration Method ◽  
Force Term ◽  
Inverse Dynamic ◽  
Inverse Dynamic Analysis ◽  
Lead Screw ◽  
Output Torque ◽  
Moving Platform ◽  
Acceleration Term

Inverse dynamic analysis of the 8-PSS redundant parallel manipulator is carried out in the exhaustive decoupled way. The required output of the torque, the power and the work of the driving motor are achieved. The whole actuating torque is divided into four terms which are caused by the acceleration, the velocity, the gravity, and the external force. It is also decoupled into the components contributed by the moving platform, the strut, the slider, the lead screw, the motor rotor-coupler, and the external force. The required powers contributed by the component of torque caused by the acceleration term, the velocity term, the gravity term, the external force term, and the powers contributed by the moving platform, the strut, the slider, the lead screw, and the motor rotor-coupler are computed respectively. For a prescribed trajectory, the required output work generated by the ith driving motor is obtained by the presented numerical integration method. Simulation for the computation of the driving motor’s output torque, power and work is illustrated.

scholarly journals On the Dynamic Properties of Flexible Parallel Manipulators in the Presence of Type 2 Singularities

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Sébastien Briot ◽  
Vigen Arakelian
Keyword(s):  
Optimal Control ◽  
Parallel Manipulator ◽  
Dynamic Properties ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Inverse Dynamic ◽  
Suggested Approach ◽  
Singular Configurations ◽  
Optimal Force

In the present paper, we expand information about the conditions for passing through Type 2 singular configurations of a parallel manipulator. It is shown that any parallel manipulator can cross the singular configurations via an optimal control permitting the favorable force distribution, i.e., the wrench applied on the end-effector by the legs and external efforts must be reciprocal to the twist along with the direction of the uncontrollable motion. The previous studies have proposed the optimal control conditions for the manipulators with rigid links and flexible actuated joints. The different polynomial laws have been obtained and validated for each examined case. The present study considers the conditions for passing through Type 2 singular configurations for the parallel manipulators with flexible links. By computing the inverse dynamic model of a general flexible parallel robot, the necessary conditions for passing through Type 2 singular configurations are deduced. The suggested approach is illustrated by a 5R parallel manipulator with flexible elements and joints. It is shown that a 16th order polynomial law is necessary for the optimal force generation. The obtained results are validated by numerical simulations carried out using the software ADAMS.

Singularity robust balancing of parallel manipulators following inconsistent trajectories

Robotica ◽  
2014 ◽  
Vol 34 (9) ◽  
pp. 2027-2038 ◽  
Author(s):  
Mustafa Özdemir
Keyword(s):  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Inverse Kinematic ◽  
Type I ◽  
Type Ii ◽  
Inverse Dynamic ◽  
Serial Manipulators ◽  
Dynamic Solution ◽  
Singular Configuration ◽  
Kinematic Singularities

SUMMARYWhen compared to serial manipulators, parallel manipulators have small workspaces mainly due to their closed-loop structure. As opposed to type I singularities (or inverse kinematic singularities) that are generally encountered at the workspace boundaries, type II singularities characteristically arise within the workspace, and around them, the inverse dynamic solution becomes unbounded. Hence, a desired trajectory passing through a type II singular position cannot be achieved by the manipulator, and its useful workspace becomes further and substantially reduced. It has been previously shown in the literature that if the trajectory is replanned in such a way that the dynamic equations of motion of the manipulator are consistent at a type II singularity, i.e. if the trajectory is consistent, then the manipulator passes through this singular configuration in a controllable manner, while the inverse dynamic solution remains finite. An inconsistent trajectory, on the other hand, is stated in the literature to be unrealizable. However, although seems a promising technique, trajectory replanning itself is also a deviation from the originally desired trajectory, and there might be cases in applications where, due to some task-specific reasons, the desired trajectory, although inconsistent, is not allowed to be replanned to satisfy the consistency conditions. In this paper, a method of singularity robust balancing is proposed for parallel manipulators passing through type II singular configurations while following inconsistent trajectories. By this means, an originally unrealizable inconsistent trajectory passing through a type II singularity can be followed without any deviation, while the required actuator forces remain bounded after the manipulator is balanced according to the design methodology presented in this study. The effectiveness of the introduced method is shown through numerical simulations considering a planar 3-DOF 2-PRR parallel manipulator under different balancing scenarios.

Computation of the Output Torque, Power and Work of the Driving Motor for a Redundant Parallel Manipulator

2011 ◽  
Vol 1 (2) ◽  
pp. 1-17 ◽  
Author(s):  
Yongjie Zhao
Keyword(s):  
External Force ◽  
Parallel Manipulator ◽  
Integration Method ◽  
Force Term ◽  
Inverse Dynamic ◽  
Inverse Dynamic Analysis ◽  
Lead Screw ◽  
Output Torque ◽  
Moving Platform ◽  
Acceleration Term

Inverse dynamic analysis of the 8-PSS redundant parallel manipulator is carried out in the exhaustive decoupled way. The required output of the torque, the power and the work of the driving motor are achieved. The whole actuating torque is divided into four terms which are caused by the acceleration, the velocity, the gravity, and the external force. It is also decoupled into the components contributed by the moving platform, the strut, the slider, the lead screw, the motor rotor-coupler, and the external force. The required powers contributed by the component of torque caused by the acceleration term, the velocity term, the gravity term, the external force term, and the powers contributed by the moving platform, the strut, the slider, the lead screw, and the motor rotor-coupler are computed respectively. For a prescribed trajectory, the required output work generated by the ith driving motor is obtained by the presented numerical integration method. Simulation for the computation of the driving motor’s output torque, power and work is illustrated.

Inverse dynamic analysis of mechanical systems in joint coordinate space

2003 ◽  
Vol 217 (1) ◽  
pp. 29-37 ◽  
Author(s):  
B H Lee
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Coordinate Space ◽  
Inverse Dynamic ◽  
Velocity Transformation ◽  
Inverse Dynamic Analysis ◽  
Joint Reaction Forces ◽  
System Equations ◽  
Cartesian Coordinate

An inverse dynamic analysis algorithm for spatial flexible mechanical systems with closed loops is developed in the relative joint coordinate space. System equations of motion and constraint acceleration equations are derived using the velocity transformation technique. An inverse velocity transformation operator, which transforms the Cartesian velocities to the relative velocities, is derived systematically, corresponding to the types of kinematic joint connecting the bodies. Using the resulting matrix, the joint reaction forces and moments are analysed in the Cartesian coordinate space. The joint coordinates and the deformation modal coordinates are used as the generalized coordinates of a flexible mechanical system. The algorithm is verified by means of two numerical examples.

scholarly journals Effect of Impeller Diameter on Dynamic Response of a Centrifugal Pump Rotor

Vibration ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 117-129
Author(s):  
Alireza Shooshtari ◽  
Mahdi Karimi ◽  
Mehrdad Shemshadi ◽  
Sareh Seraj
Keyword(s):  
Dynamic Response ◽  
Centrifugal Pump ◽  
Model Updating ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Oil Refinery ◽  
Centrifugal Pumps ◽  
Concentrated Mass ◽  
Inverse Dynamic ◽  
Pump Impeller

This paper investigates the effect of impeller diameter on the dynamic response of a centrifugal pump using an inverse dynamic method. For this purpose, the equations of motion of the shaft and the impeller are derived based on Timoshenko beam theory considering the impeller as a concentrated mass disk. For practical modeling, the model of Jones and Harris is added to the equation to include the effect of bearings. As a case study, the model is applied to a process pump used in an oil refinery. Computing the eigenvalues of the model and comparing them with the natural frequencies of the structure, the model updating of the problem is performed through an indirect method. Three impellers with different diameters are applied to the updated model. The results show that increasing the diameter of the pump impeller can increase the amplitude of vibration up to 52% at critical speeds of the rotor. It is found that in addition to the hydraulic condition and efficiency, the impeller diameter should be considered as an important factor in the selection of centrifugal pumps.

Singularity and Controllability Analysis of Parallel Manipulators

1998 ◽  
Author(s):  
Prasun Choudhury ◽  
Ashitava Ghosal
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Transformation Matrix ◽  
Constraint Forces ◽  
Numerical Examples ◽  
Cartesian Space ◽  
Force Transformation

Abstract This paper presents a study of kinematic and force singularities and their relationship to the controllability of planar and spatial parallel manipulators. Parallel manipulators are classified according to their degrees of freedom, number of output Cartesian variables used to describe their motion and the number of actuated joint inputs. The singularities in the workspace of a parallel manipulator are studied by considering the force transformation matrix which maps the forces and torques in joint space to output forces and torques in Cartesian space. The uncontrollable regions in the workspace of the parallel manipulator are obtained by deriving the equations of motion in terms of Cartesian variables and by using techniques from Lie Algebra. We show that when the number of actuated joint inputs is equal to the number of output Cartesian variables, and the force transformation matrix loses rank, the parallel manipulator is uncontrollable. For the case of manipulators where the number of joint inputs is less than the number of output Cartesian variables, if the constraint forces and torques (represented by the Lagrange multipliers) become infinite, the force transformation matrix loses rank. Finally, we show that the singular and uncontrollable regions in the workspace of a parallel manipulator can be reduced by adding redundant joint actuators and links. The results are illustrated with the help of numerical examples where we plot the singular and uncontrollable regions of parallel manipulators belonging to the above mentioned classes.

Closed-Form Forward Dynamic Equations of 6-DOF PUS Type Parallel Manipulators

2000 ◽  
Author(s):  
Jong-Phil Kim ◽  
Jeha Ryu
Keyword(s):  
Closed Form ◽  
Parallel Manipulator ◽  
Control Strategies ◽  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Simulation Software ◽  
Dynamic Equations ◽  
Constant Length ◽  
Euler Approach ◽  
Six Degree Of Freedom

Abstract This paper presents closed-form forward dynamic equations of six degree-of-freedom HexaSlide type parallel manipulators. The HexaSlide type parallel manipulators are characterized by an architecture with constant-length links that are attached to moving sliders on the ground and to a mobile platform. Based on the kinematic analysis, forward dynamic equations of motion of the parallel manipulator are derived by the Newton-Euler approach. In this derivation, joint frictions as well as all link inertia are included. The correctness of derived dynamic equations is validated by a commercial dynamic simulation software. The kinematic and dynamic equations may be used in the computer simulation of various control strategies.

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