Explicit dynamic equations for a chain of flexible links

1992 ◽  
Vol 9 (8) ◽  
pp. 1083-1094
Author(s):  
Zhongping Deng ◽  
Liping Wang
Keyword(s):  
Dynamic Equations ◽  
Flexible Links ◽  
A Chain ◽  
Explicit Dynamic

Dynamics of Chain of Flexible Links

1988 ◽  
Vol 110 (4) ◽  
pp. 410-415 ◽  
Author(s):  
M. Benati ◽  
A. Morro
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Lagrangian Approach ◽  
The Other ◽  
Dynamic Equations ◽  
Flexible Links ◽  
A Chain

A Lagrangian approach is developed for the dynamics of a chain with flexible links. Each link is modeled as a system with a finite number of degrees of freedom, one of them describing the rotation, the other ones the flexibility. While the approach is developed for chains with any numbers of links, the dynamic equations are written explicitly for a chain with two links and a payload.

Formulation of Equations of Motion for a Chain of Flexible Links Using Hamilton’s Principle

1994 ◽  
Vol 116 (1) ◽  
pp. 81-88 ◽  
Author(s):  
M. Benati ◽  
A. Morro
Keyword(s):  
Boundary Conditions ◽  
Finite Number ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Dynamic Equations ◽  
Relative Deformation ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Flexible Links ◽  
A Chain

The dynamic equations of a chain of flexible links are determined by means of Hamilton’s principle. First a continuous model is adopted and the boundary conditions are determined, along with the partial differential equations of motion. Then a model with a finite number of degrees of freedom is set up. The configuration of each link is described through the line which joins the end points and the relative deformation is described in terms of appropriate trial functions. The boundary conditions are incorporated into a set of basic trial functions. The time-dependent coefficients of the remaining shape functions play the role of Lagrangian coordinates. The dynamic equations are then derived and the procedure is contrasted with other methods for reduction of a system of links to a system with a finite number of degrees of freedom.

Optimal trajectory planning and sliding mode control for robots using evolution strategy

Robotica ◽  
2000 ◽  
Vol 18 (4) ◽  
pp. 423-428 ◽  
Author(s):  
Young-Kiu Choi ◽  
Jin-Hyun Park ◽  
Hyun-Sik Kim ◽  
Jung Hwan Kim
Keyword(s):  
Trajectory Planning ◽  
Sliding Mode ◽  
Evolution Strategy ◽  
Minimum Time ◽  
Dynamic Equations ◽  
Dynamic Constraints ◽  
Planning And Control ◽  
Explicit Dynamic ◽  
And Control ◽  
Kinematic Approach

Although robots have some kinematic and dynamic constraints such as the limits of the position, velocity, acceleration, jerk, and torque, they should move as fast as possible to increase the productivity. Researches on the minimum-time trajectory planning and control based on the dynamic constraints assume the availability of full dynamics of robots. However, the dynamic equation of robot may not often be exactly known. In this case, the kinematic approach for the minimum-time trajectory planning is more meaningful. We also have to construct a controller to track precisely the minimum-time trajectory. But, finding a proper controller is also difficult if we do not know the explicit dynamic equations of a robot.This paper describes an optimization of trajectory planning based on a kinematic approach using the evolution strategy (ES), as well as an optimization of a sliding mode tracking controller using ES for a robot without dynamic equations.

SCALAR FORM OF DYNAMIC EQUATIONS FOR A TOPOLOGICALLY UNIFORM 3D-CHAIN

1995 ◽  
Vol 19 (4) ◽  
pp. 397-416
Author(s):  
O. Vinogradov
Keyword(s):  
Rigid Body ◽  
Dynamic Equations ◽  
Inertial Coordinate System ◽  
Scalar Form ◽  
Kinematic Constraints ◽  
One Dimensional ◽  
D’Alembert Principle ◽  
Translational Degree ◽  
A Chain ◽  
System Topology

A topologically uniform 3D-chain is defined as a system of one-dimensional links connected by spherical joints. In addition each link has an internal translational degree of freedom along its axis. Such a chain can be viewed as a generic manipulator so that any specific type of the latter can be obtained from this chain by imposing additional kinematic constraints. It is shown that for the introduced chain the dynamic equations can be derived in an explicit scalar form. The derivation is based on the D’Alembert principle, inertial coordinate system and direct utilization of the path matrix describing the system topology. An example of application of the results to a 2-DOF rigid-body manipulator is given.

A Lagrangian Formulation of the Dynamic Model for Flexible Manipulator Systems

1988 ◽  
Vol 110 (2) ◽  
pp. 175-181 ◽  
Author(s):  
K. H. Low ◽  
M. Vidyasagar
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Natural Extension ◽  
Flexible Manipulator ◽  
Dynamic Equations ◽  
Continuous Systems ◽  
Flexible Link ◽  
Flexible Links ◽  
Generalized Coordinates ◽  
Kinetic And Potential Energies

This paper presents a procedure for deriving dynamic equations for manipulators containing both rigid and flexible links. The equations are derived using Hamilton’s principle, and are nonlinear integro-differential equations. The formulation is based on expressing the kinetic and potential energies of the manipulator system in terms of generalized coordinates. In the case of flexible links, the mass distribution and flexibility are taken into account. The approach is a natural extension of the well-known Lagrangian method for rigid manipulators. Properties of the dynamic matrices, which lead to a less computation, are shown. Boundary-value problems of continuous systems are briefly described. A two-link manipulator with one rigid link and one flexible link is analyzed to illustrate the procedure.

Analytical dynamic modeling of Delta robot with experimental verification

2020 ◽  
Vol 234 (3) ◽  
pp. 623-630
Author(s):  
Farshid Asadi ◽  
Ali Heydari
Keyword(s):  
Dynamic Model ◽  
Virtual Work ◽  
Time Derivative ◽  
Dynamic Equations ◽  
Robot Dynamics ◽  
Jacobian Matrices ◽  
Acceleration Analysis ◽  
Delta Robot ◽  
Explicit Dynamic ◽  
And Control

In this paper, an explicit dynamic model of Delta robot is obtained analytically. The main contribution of this work is that, unlike existing prior work, the final dynamics model is given directly in the form of [Formula: see text], with explicit expressions for M, C and G. This is of great importance, since many advanced control techniques like Optimal Control need dynamic model in an explicit form, i.e. time derivative of state vector given explicitly in terms of the states and control vectors. To this goal, first, velocity and acceleration analysis is done by differentiating robot's geometrical loops directly. Then, Jacobian matrices are calculated to have kinematic relations in a more compact form. After that, principle of virtual work is implemented to derive the dynamic equations. In this part, Jacobian matrices are substituted into dynamic model. This is unlike other referenced works on Delta robot dynamics that need to continue the derivation in symbolic software or derive the model implicitly. Using Jacobians, dramatically simplifies the final explicit dynamic model. Therefore, the final dynamic equations are calculated in a straightforward manner without any use of symbolic calculation software. After all, the presented model is verified with an experimental setup. The model shows good accuracy in terms of torque prediction.

CUSTOMIZED SCALAR DYNAMIC EQUATIONS FOR ROBOTIC MANIPULATORS

1996 ◽  
Vol 20 (4) ◽  
pp. 401-420
Author(s):  
Oleg Vinogradov
Keyword(s):  
Rigid Body ◽  
Computer Simulations ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Dynamic Equations ◽  
Governing Equations ◽  
Scalar Form ◽  
Kinematic Constraints ◽  
One Dimensional ◽  
A Chain

A robotic manipulator is considered as a reduction of a topologically uniform 3D-chain which is defined as a system of one-dimensional links connected by spherical joints. It has been shown in (4) that for the introduced chain the dynamic equations can be derived in an explicit scalar form. Such a chain can be viewed as a generic manipulator so that any specific type of the latter can be obtained from this chain by imposing additional kinematic constraints. It is shown in the paper that for practically all joints the governing equations for the chain and the constraints equations can be solved together resulting in an explicit scalar form of equations for a given manipulator. This form of equations has a potential for more efficient computer simulations. An application of the results to a 3-DOF rigid-body manipulator is given.

scholarly journals Building dynamic equations of manipulator with flexible links

2017 ◽  
Vol 20 (K1) ◽  
pp. 28-34
Author(s):  
Duong Xuan Bien ◽  
Chu Anh My ◽  
Phan Bui Khoi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Control System ◽  
Dynamic Modeling ◽  
General Model ◽  
Horizontal Plane ◽  
Dynamic Equations ◽  
Initial Moment ◽  
Dynamic Behaviors ◽  
Flexible Links

This paper presents the research of general model and building dynamic equations of two flexible links manipulator motion in the horizontal plane. Dynamic modeling is considered with adding factors which are payload, elastic friction, mass and initial moment of rotors. So it is closed to reality. Dynamic equations are derived through finite element method based on Lagrange approach. Dynamic behaviors of the system with payload were simulated like a specific example. The results can be used to building the control system which increases accuracy position of manipulators under influence of elastic displacements of links.

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