Dynamic Model Of Parallel Manipulator Research Articles

Dynamic modeling of parallel manipulators based on Lagrange–D’Alembert formulation and Jacobian/Hessian matrices

This paper describes the development of a dynamic model for parallel manipulators based on the Lagrange–D’Alembert equation, the Hessian matrix of the kinetic energy of the manipulator, and the Jacobian/Hessian matrices of the constraint equations. The model generates the forward and inverse dynamics formulations of parallel manipulators. First, the kinematic relations between the input actuated variables and the output variables are defined in terms of the Jacobian and Hessian matrices of the constraint equations. Then, a new form of Lagrange–D’Alembert equation is introduced and used to derive the dynamic model of parallel manipulators. In the present model, the inertia, centrifugal, and Coriolis generalized forces/torques are obtained directly from Hessian matrix of the kinetic energy of the manipulator. The developed model is simple, straightforward, and appropriate for parallel processing techniques as the elements of the Jacobian and Hessian matrices can be calculated simultaneously. The developed model is validated using the conservation of work and energy principle. A trajectory tracking control of a simple 3RRR planar parallel manipulator is used to illustrate the developed model.

Kinematic and Dynamic Analysis of 3PUU Parallel Manipulator for Medical Applications

This paper presents an explicit work on developing a parallel manipulator for medical application. There are many applications in medicine that requires the technology of robotics like injecting electrodes, drilling of bone, medical transportation, to carry out different tests and so on. Surgeons divert their focus on improving the quality of the surgical procedure that includes accuracy, security, low morbidity and mortality. This work mainly concentrates on designing and developing a kinematic and dynamic model of parallel manipulator for bone drilling application which is required for prosthetics operations. According to the requirement of the application a three prismatic-universal-universal (3PUU) parallel manipulator is designed which rotates about x and y axis and translates along z axis. This research work involves in developing a conceptual design, deriving kinematics both inverse and forward, workspace and dynamics of the parallel manipulator. Inverse kinematics is obtained by the geometrical approach whereas inverse dynamics is obtained using Langrangian method. Further, the tool inverse kinematic solutions, overall workspace, dynamics of the three legs are determined. This study will help the researchers for the further development of parallel manipulators in medical assistance.

Solving the dynamic equations of a 3-PRS Parallel Manipulator for efficient model-based designs

Abstract. Introduction of parallel manipulator systems for different applications areas has influenced many researchers to develop techniques for obtaining accurate and computational efficient inverse dynamic models. Some subject areas make use of these models, such as, optimal design, parameter identification, model based control and even actuation redundancy approaches. In this context, by revisiting some of the current computationally-efficient solutions for obtaining the inverse dynamic model of parallel manipulators, this paper compares three different methods for inverse dynamic modelling of a general, lower mobility, 3-PRS parallel manipulator. The first method obtains the inverse dynamic model by describing the manipulator as three open kinematic chains. Then, vector-loop closure constraints are introduced for obtaining the relationship between the dynamics of the open kinematic chains (such as a serial robot) and the closed chains (such as a parallel robot). The second method exploits certain characteristics of parallel manipulators such that the platform and the links are considered as independent subsystems. The proposed third method is similar to the second method but it uses a different Jacobian matrix formulation in order to reduce computational complexity. Analysis of these numerical formulations will provide fundamental software support for efficient model-based designs. In addition, computational cost reduction presented in this paper can also be an effective guideline for optimal design of this type of manipulator and for real-time embedded control.

Dynamic Analysis and Optimization of Parallel Manipulator

Electromechanical coupling dynamic model of parallel manipulator is a kind of a complicated electromechanical system which is multi‐input, multi‐output, nonlinear and strong coupling. There is not a perfect method to calculate dynamic modeling and simulation of parallel manipulator at present. 6UPS‐parallel manipulator dynamic model was set up by Lagrange method; PID position controller was designed; and the controller parameters were optimized by inertia weight adaptive particle swarm optimization in the article. It was proved that the modeling of electromechanical coupling dynamic model was right and the manipulator was controlled well by the controller through the simulation result of computer.