Symbolic derivation of dynamic equations of motion for robot manipulators using Piogram symbolic method

1988 ◽  
Vol 4 (6) ◽  
pp. 599-609 ◽  
Author(s):  
Pi-Ying Cheng ◽  
Ching-I Weng ◽  
Chao-Kuang Chen
Keyword(s):  
Robot Manipulators ◽  
Equations Of Motion ◽  
Dynamic Equations ◽  
Symbolic Method

Automatic Formulation of Dynamic Equations of Motion of Robot Manipulators

1988 ◽  
Vol 202 (6) ◽  
pp. 397-404 ◽  
Author(s):  
D Pan ◽  
R S Sharp
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Chain Structure ◽  
Algebraic Manipulation ◽  
Dynamic Equations ◽  
Open Chain ◽  
Scalar Form ◽  
Memory Space ◽  
Manipulation Language

Based on the use of homogeneous transformation matrices with Denavit-Hartenberg notation and the Lagrangian formulation method, a general computer program ROBDYN.RED for the symbolic derivation of dynamic equations of motion for robot manipulators has been developed and is discussed in this paper. The program is developed by using REDUCE, an algebraic manipulation language, and is versatile for open-chain structure robot manipulators with any number of degrees of freedom and with any combination of types of joint. Considerations are also given to saving computer memory space required for execution and to minimizing the runtime. Several examples are included to demonstrate the use of the program. Equations of motion in scalar form can be automatically transferred to FORTRAN format for later numerical simulations. The efficiency of the resulting equations in terms of numerical integration is also discussed and some further developments to improve the efficiency are suggested.

On the Properties of a Dynamic Model of Flexible Robot Manipulators

1998 ◽  
Vol 120 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Marco A. Arteaga
Keyword(s):  
Dynamic Model ◽  
Structural Properties ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Control Design ◽  
Flexible Manipulator ◽  
Robot Dynamics ◽  
Flexible Link ◽  
Flexible Robot

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.

Cayley kinematics and the Cayley form of dynamic equations

2005 ◽  
Vol 461 (2055) ◽  
pp. 761-781 ◽  
Author(s):  
Andrew J. Sinclair ◽  
John E. Hurtado
Keyword(s):  
Euler Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
Matrix Form ◽  
Dynamic Equations ◽  
Cayley Transform ◽  
Higher Dimensional ◽  
The Matrix ◽  
General Motion

The Cayley transform and the Cayley–transform kinematic relationships are an important and fascinating set of results that have relevance in N –dimensional orientations and rotations. In this paper these results are used in two significant ways. First, they are used in a new derivation of the matrix form of the generalized Euler equations of motion for N –dimensional rigid bodies. Second, they are used to intimately relate the motion of general mechanical systems to the motion of higher–dimensional rigid bodies. This approach can be used to describe an enormous variety of systems, one example being the representation of general motion of an N –dimensional body as pure rotations of an ( N + 1)–dimensional body.

Dynamic Modeling of Robotic Fish Caudal Fin With Electrorheological Fluid-Enabled Tunable Stiffness

2015 ◽  
Author(s):  
Sanaz Bazaz Behbahani ◽  
Xiaobo Tan
Keyword(s):  
Equations Of Motion ◽  
Electrorheological Fluid ◽  
Robotic Fish ◽  
Dynamic Equations ◽  
The Finite Element Method ◽  
Modeling Framework ◽  
Caudal Fin ◽  
Body Theory ◽  
Tunable Stiffness ◽  
Er Fluid

In this study, we investigate the modeling framework for a robotic fish actuated by a flexible caudal fin, which is filled with electrorheological (ER) fluid and thus enables tunable stiffness. This feature can be used in optimizing the robotic fish speed or maneuverability in different operating regimes. The robotic fish is assumed to be anchored and the flexible tail undergoes undulation activated by a servomotor at the base. Lighthill’s large-amplitude elongated-body theory is used to calculate the hydrodynamic force on the caudal fin, and Hamilton’s principle is used to derive the dynamic equations of motion of the caudal fin. The dynamic equations are then discritized using the finite element method, to obtain an approximate numerical solution. In particular, simulation is conducted to understand the influence of the applied electric field on the stiffness and thrust performance of the caudal fin.

Dynamics of the Planetary Roller Screw Mechanism

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Matthew H. Jones ◽  
Steven A. Velinsky ◽  
Ty A. Lasky
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Equations Of Motion ◽  
Viscous Friction ◽  
Contact Angles ◽  
Dynamic Equations ◽  
Roller Screw ◽  
Angular Velocities ◽  
Screw Mechanism ◽  
Lagrange’S Method

This paper develops the dynamic equations of motion for the planetary roller screw mechanism (PRSM) accounting for the screw, rollers, and nut bodies. First, the linear and angular velocities and accelerations of the components are derived. Then, their angular momentums are presented. Next, the slip velocities at the contacts are derived in order to determine the direction of the forces of friction. The equations of motion are derived through the use of Lagrange's Method with viscous friction. The steady-state angular velocities and screw/roller slip velocities are also derived. An example demonstrates the magnitude of the slip velocity of the PRSM as a function of both the screw lead and the screw and nut contact angles. By allowing full dynamic simulation, the developed analysis can be used for much improved PRSM system design.

General Equations of a Helical Spring With a Cup Damper and Static Verification

1997 ◽  
Vol 119 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Ming Hsun Wu ◽  
Jing Yuan Ho ◽  
Wensyang Hsu
Keyword(s):  
Experimental Data ◽  
Pitch Angle ◽  
Equations Of Motion ◽  
Maximum Error ◽  
Dynamic Equations ◽  
Helical Spring ◽  
Static Force ◽  
Static Verification ◽  
Simulation Results ◽  
Force Displacement

In this study, we derive the general equations of motion for the helical spring with a cup damper by considering the damper’s dilation and varying pitch angle of the helical spring. These dynamic equations are simplified to correlate with previous models. The static force-displacement relation is also derived. The extra stiffness due to the damper’s dilation considered in the force-displacement relation is the first such modeling in this area. In addition, a method is presented to predict the compressing spring’s coil close length and is then verified by experimental data. Moreover, the simulation results of the static force-displacement relation are found to correspond to the experimental data. The maximum error is around 0.6 percent.

Analysis of Varying Natural Frequencies and Damping Ratios of a Sample Parallel Manipulator Throughout its Workspace Using Linearized Equations of Motion

2001 ◽  
Author(s):  
Kris Kozak ◽  
Imme Ebert-Uphoff ◽  
William Singhose
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Parallel Architecture ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Dynamic Equations ◽  
Extreme Variation

Abstract This article investigates the dynamic properties of robotic manipulators of parallel architecture. In particular, the dependency of the dynamic equations on the manipulator’s configuration within the workspace is analyzed. The proposed approach is to linearize the dynamic equations locally throughout the workspace and to plot the corresponding natural frequencies and damping ratios. While the results are only applicable for small velocities of the manipulator, they present a first step towards the classification of the nonlinear dynamics of parallel manipulators. The method is applied to a sample manipulator with two degrees-of-freedom. The corresponding numerical results demonstrate the extreme variation of its natural frequencies and damping ratios throughout the workspace.

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