Dynamic Modeling of a Non-Redundant Spatial Mobile Manipulator

2001 ◽  
Author(s):  
James M. Stiles ◽  
Jae H. Chung ◽  
Steven A. Velinsky
Keyword(s):  
High Speed ◽  
Robot Manipulator ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
High Mobility ◽  
Mobile Manipulator ◽  
Mobile Manipulators ◽  
Mobile Platforms ◽  
Wheel Slip ◽  
Kinematic Models

Abstract Mobile manipulators are comprised of robot manipulators mounted upon mobile platforms which allow for both high mobility and dexterous manipulation ability. Although much research has been performed in the area of motion control of mobile manipulators, previous developed models are typically simplified and assume only planar motion and/or holonomic constraints. In this work, the equations of motion of a three dimensional non-redundant wheeled-vehicle based mobile manipulator system are developed using a Newton-Euler formulation. This model incorporates a complex tire model which accounts for tire slip and is thus applicable to high speed and high load applications. The model is systematically exercised to examine the dynamic interaction effects between the mobile platform and the robot manipulator, to illustrate the effects of wheel slip on system performance, and to establish bounds on the efficacy of the simplified existing kinematic models.

A Compliant Double Pin Track Link Model for Multibody Tracked Vehicles

1999 ◽  
Author(s):  
J. H. Choi ◽  
D. S. Bae ◽  
H. S. Ryu
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
High Mobility ◽  
Contact Forces ◽  
Integration Step ◽  
Step Size ◽  
Tracked Vehicles ◽  
Accelerated Motion ◽  
Pin Track

Abstract It is the objective of this investigation to develop compliant double pin track link models and investigate the use of these models in the dynamic analysis of high mobility tracked vehicles. There are two major difficulties encountered in developing the compliant track models discussed in this paper. The first is due to the fact that the integration step size must be kept small in order to maintain the numerical stability of the solution. This solution includes high oscillatory signals resulting from the impulsive contact forces and the use of stiff compliant elements to represent the joints between the track links. The characteristics of the compliant, elements used in this investigation to describe the track joints are measured experimentally. The second difficulty encountered in this investigation is due to the large number of the system equations of motion of the three dimensional multibody tracked vehicle model. The dimensionality problem is solved by decoupling the equations of motion of the chassis subsystem and the track subsystems. Recursive methods are used to obtain a minimum set of equations for the chassis subsystem. Several simulation scenarios including an accelerated motion, high speed motion, braking, and turning motion of the high mobility vehicle are tested in order to demonstrate the effectiveness and validity of the methods proposed in this investigation.

An Efficient Numerical Method for Dynamic Interaction Analysis of Shinkansen Train and Railway Structure During an Earthquake

2007 ◽  
Author(s):  
M. Tanabe ◽  
N. Matsumoto ◽  
H. Wakui ◽  
M. Sogabe ◽  
H. Okuda ◽  
...  
Keyword(s):  
Numerical Method ◽  
High Speed ◽  
Large Scale ◽  
Interaction Analysis ◽  
Plastic Material ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Material Model ◽  
Dynamic Interaction ◽  
Contact Dynamics

In this paper, a simple and efficient numerical method to solve for the dynamic interaction of a Shinkansen train (high-speed train in Japan) and railway structure during an earthquake is given. The motion of the train is modeled in multibody dynamics with nonlinear springs and dampers used to connect components. An efficient mechanical model for contact dynamics between wheel and rail during an earthquake is presented. The railway structure is modeled with various finite elements. A three-dimensional nonlinear spring element based on a trilinear elastic-plastic material model is given for the concrete railway structure during an earthquake. A loop structure model has been devised to obtain an approximated combined motion of the train and railway structure during an earthquake. A modal method has been developed to solve large-scale nonlinear equations of motion of the train and railway structure effectively. Based on the present method, a computer program DIASTARS for the dynamic interaction of a Shinkansen train and railway structure during an earthquake has been developed. Numerical examples are demonstrated.

Modal Analysis of Ballooning Strings With Small Sag

1999 ◽  
Author(s):  
Rongjun Fan ◽  
Sushil K. Singh ◽  
Christopher D. Rahn
Keyword(s):  
Steady State ◽  
High Speed ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Theoretical Predictions ◽  
Nonlinear Equations Of Motion

Abstract During the manufacture and transport of textile products, yarns are rotated at high speed and form balloons. The dynamic response of the balloon to varying rotation speed, boundary excitation, and disturbance forces governs the quality of the associated process. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three dimensional nonlinear equations of motion are simplified via small steady state displacement (sag) and vibration assumptions. Axial vibration is assumed to propagate instantaneously or in a quasistatic manner. Galerkin’s method is used to calculate the mode shapes and natural frequencies of the linearized equations. Experimental measurements of the steady state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.

Ship Motion Computations Using a High Froude Number Time Domain Strip Theory

2006 ◽  
Vol 50 (01) ◽  
pp. 15-30
Author(s):  
D. S. Holloway ◽  
M. R. Davis
Keyword(s):  
Froude Number ◽  
Time Domain ◽  
High Speed ◽  
Equations Of Motion ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Viscous Effects ◽  
Strip Theory ◽  
Large Amplitude Motions ◽  
The Time Domain

High-speed strip theories are discussed, and a time domain formulation making use of a fixed reference frame for the two-dimensional fluid motion is described in detail. This, and classical (low-speed) strip theory, are compared with the experimental results of Wellicome et al. (1995) up to a Froude number of 0.8, as well as with our own test data for a semi-SWATH, demonstrating the marked improvement of the predictions of the former at high speeds, while the need to account for modest viscous effects at these speeds is also argued. A significant contribution to time domain computations is a method of stabilizing the integration of the ship's equations of motion, which are inherently unstable due to feedback from implicit added mass components of the hydrodynamic force. The time domain high-speed theory is recommended as a practical alternative to three-dimensional methods. It also facilitates the investigation of large-amplitude motions with stern or bow emergence and forms a simulation base for the investigation of ride control systems and local or global loads.

The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports

1969 ◽  
Vol 91 (4) ◽  
pp. 1105-1113 ◽  
Author(s):  
E. J. Gunter ◽  
P. R. Trumpler
Keyword(s):  
Internal Friction ◽  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Analog Computer ◽  
Three Dimensional Model ◽  
Stiffness Properties ◽  
Stiffness Characteristics ◽  
The Stability ◽  
Internal Rotor

This paper evaluates the stability of the single mass rotor with internal friction on damped, anisotropic supports. The paper shows under what conditions the rotor stability may be improved by an undamped support with anisotropic stiffness properties. A three dimensional model is presented to show the influence of rotor and support stiffness characteristics on stability. Curves are also presented on how support damping may also improve or even reduce rotor stability. An analog computer solution of the governing equations of motion is presented showing the shaft transient motion for various speed ranges, and also plots of the rotor steady state motion are given for various speeds up to and including the stability threshold. The analysis is used to explain many of the experimental observations of B. L. Newkirk concerning stability due to internal rotor friction.

scholarly journals The impact of pelvic lateral rotation on hindlimb kinematics and stride length in the red-legged running frog, Kassina maculata

2019 ◽  
Vol 6 (5) ◽  
pp. 190060 ◽  
Author(s):  
Amber J. Collings ◽  
Laura B. Porro ◽  
Cameron Hill ◽  
Christopher T. Richards
Keyword(s):  
High Speed ◽  
Stride Length ◽  
Reference Frames ◽  
Comparative Anatomy ◽  
Three Dimensional ◽  
Video Data ◽  
The Body ◽  
Kinematic Models ◽  
Lateral Rotation ◽  
The Impact

Some frog species, such as Kassina maculata (red-legged running frog), use an asynchronous walking/running gait as their primary locomotor mode. Prior comparative anatomy work has suggested that lateral rotation of the pelvis improves walking performance by increasing hindlimb stride length; however, this hypothesis has never been tested. Using non-invasive methods, experimental high-speed video data collected from eight animals were used to create two three-dimensional kinematic models. These models, each fixed to alternative local anatomical reference frames, were used to investigate the hypothesis that lateral rotation of the mobile ilio-sacral joint in the anuran pelvis plays a propulsive role in walking locomotion by increasing hindlimb stride length. All frogs used a walking gait (duty factor greater than 0.5) despite travelling over a range of speeds (0.04–0.23 m s −1 ). The hindlimb joint motions throughout a single stride were temporally synchronized with lateral rotation of the pelvis. The pelvis itself, on average, underwent an angular excursion of 12.71° (±4.39°) with respect to the body midline during lateral rotation. However, comparison between our two kinematic models demonstrated that lateral rotation of the pelvis only increases the cranio-caudal excursion of the hindlimb modestly. Thus, we propose that pelvic lateral rotation is not a stride length augmenting mechanism in K. maculata .

Free Vibration Analysis of Rotating Structures by One-Dimensional, Variable Kinematic Theories

2013 ◽  
Author(s):  
Erasmo Carrera ◽  
Matteo Filippi ◽  
Enrico Zappino
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Weak Form ◽  
The Finite Element Method ◽  
Kinematic Models ◽  
Gyroscopic Effects ◽  
Dimensional Variable ◽  
Structural Theories ◽  
Beam Theories

In this paper, Carrera’s Unified Formulation (CUF) is extended to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation which offers a procedure to obtain refined structural theories that account for variable kinematic description. These theories are obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor’s polynomials of N-order, in which N is a free parameter. The linear case (N = 1) permits us to obtain classical beam theories while higher order expansions could lead to three-dimensional description of dynamic response of both rotors and centrifugally stiffened beams. The Finite Element method is used to derive the weak form of the three-dimensional differential equations of motion in term of fundamental nuclei, whose forms do not depend on the approximation used (N). The present formulations include gyroscopic effects and stiffening due to centrifugal stresses. In order to verify the accuracy of the new theories, several analyses are carried out and the results are compared with solutions presented in the literature in graphical and numerical form. The advantages of the variable kinematic models are evident especially when shafts with deformable discs and thin-walled rotating beams made up with composite materials are studied.

scholarly journals Collision-Free Trajectory Planning for Mobile Manipulators Subject to Control Constraints

2014 ◽  
Vol 61 (1) ◽  
pp. 35-55
Author(s):  
Grzegorz Pajak ◽  
Iwona Pajak
Keyword(s):  
Three Dimensional ◽  
Nonholonomic Constraints ◽  
Mobile Manipulator ◽  
Reference Trajectory ◽  
Mobile Manipulators ◽  
Control Constraints ◽  
Redundancy Resolution ◽  
Manipulability Measure ◽  
Point To Point ◽  
And Control

Abstract A method of planning collision-free trajectory for a mobile manipulator tracking a line section path is presented. The reference trajectory of a mobile platform is not needed, mechanical and control constraints are taken into account. The method is based on a penalty function approach and a redundancy resolution at the acceleration level. Nonholonomic constraints in a Pfaffian form are explicitly incorporated to the control algorithm. The problem is shown to be equivalent to some point-to-point control problem whose solution may be easier determined. The motion of the mobile manipulator is planned in order to maximise the manipulability measure, thus to avoid manipulator singularities. A computer example involving a mobile manipulator consisting of a nonholonomic platform (2,0) class and a 3 DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.

Generalized Equations of Motion for the Dynamic Analysis of Elastic Mechanism Systems

1984 ◽  
Vol 106 (4) ◽  
pp. 243-248 ◽  
Author(s):  
D. A. Turcic ◽  
Ashok Midha
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Single Type ◽  
Generalized Equations ◽  
Element Analysis ◽  
Beam Elements ◽  
Elastic Mechanism ◽  
Element Type

Until recently, vibration effects have generally been neglected in the design of high-speed machines and mechanisms. This has been primarily due to the complexity of the mathematical analysis of mechanisms with elastic links. With the advent of high-speed computers and structural dynamics techniques, such as finite element analysis, this is no longer regarded as such a formidable task. To date, with few exceptions, the analysis of elastic mechanism systems have been limited to a single type of mechanism (i.e., a four-bar or slider-crank) modeled with a small number of simple finite elements (usually beam elements). This paper develops the generalized equations of motion for elastic mechanism systems by utilizing finite element theory. The derivation and final form of the equations of motion provide the capability to model a general two- or three-dimensional complex elastic mechanism, to include the nonlinear rigid-body and elastic motion coupling terms in a general representation, and to allow any finite element type to be utilized in the model. A discussion of a solution method, applications, as well as an experimental investigation of an elastic four-bar mechanism will be presented in subsequent publications.

The Dual Inertia Operator and Its Application to Robot Dynamics

1994 ◽  
Vol 116 (4) ◽  
pp. 1089-1095 ◽  
Author(s):  
V. Brodsky ◽  
M. Shoham
Keyword(s):  
Rigid Body ◽  
Robot Manipulator ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Three Dimensional ◽  
Dynamic Equations ◽  
Robot Dynamics ◽  
Dual Vector ◽  
Vector Algebra ◽  
Vector Part

The principle of transference states that when dual numbers replace real ones all laws of vector algebra, which describe the kinematics of rigid body with one point fixed, are also valid for motor algebra, which describes a free rigid body. No such direct extension exists, however, for dynamics. Rather, the inertia binor is used to obtain the dual momentum, from which the dual equations of motion are derived. This raises the dual dynamic equations to six dimensions, and in fact, does not act on the dual vector as a whole, but on its real and dual parts as two distinct real vectors. Moreover, in order to obtain the dual force as a derivative of the dual momentum in a correct order, real and dual parts have to be artificially interchanged. In this investigation the dual inertia operator, which allows direct relation of dual momentum to dual velocity, is introduced. It gives the mass a dual property which has the inverse sense of Clifford’s dual unit, namely, it reduces a motor to a rotor proportional to the vector part of the former. In a way analogous to the principle of transference, the same equation of momentum and its time derivative, which holds for a linear motion, holds for both linear and angular motion of a rigid body if dual force, dual velocity, and dual inertia replace their real counterparts. It is shown that by systematic application of the dual inertia for derivation of the dual momentum and the dual energy, both Newton-Euler and Lagrange formulations of equations of motion are obtained in a complete three-dimensional dual form. As an example, these formulations are used to derive the inverse dual dynamic equations of a robot manipulator.

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