Singularity-Free Joint Actuation in Omnidirectional Mobile Platforms With Powered Offset Caster Wheels

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Denny Oetomo ◽  
Marcelo H. Ang
Keyword(s):  
Equations Of Motion ◽  
Mobile Platform ◽  
Mobile Platforms ◽  
Free Condition ◽  
Singular Configurations ◽  
Workspace Analysis ◽  
Equations Of Motions

This paper presents the analysis of singularity and motion capability of a mobile platform articulated by offset powered caster wheels. Specifically, it presents the analysis of the equations of motion resulting in the sufficient and necessary actuation condition to yield a workspace that is entirely free of singular configurations. This paper shows that powering both the steer and drive joints on two sets of offset caster wheels in a mobile platform guarantees a singularity-free condition throughout the entire workspace. Analysis and discussion on equations of motions that lead to this result are presented.

Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops

1989 ◽  
Author(s):  
P. E. Nikravesh ◽  
G. Gim
Keyword(s):  
Equations Of Motion ◽  
Transformation Matrix ◽  
Velocity Transformation ◽  
Constraint Equations ◽  
Advantages And Disadvantages ◽  
Lagrange Multiplier Technique ◽  
Joint Coordinates ◽  
Minimum Number ◽  
Kinematic Loops ◽  
Equations Of Motions

Abstract This paper presents a systematic method for deriving the minimum number of equations of motion for multibody system containing closed kinematic loops. A set of joint or natural coordinates is used to describe the configuration of the system. The constraint equations associated with the closed kinematic loops are found systematically in terms of the joint coordinates. These constraints and their corresponding elements are constructed from known block matrices representing different kinematic joints. The Jacobian matrix associated with these constraints is further used to find a velocity transformation matrix. The equations of motions are initially written in terms of the dependent joint coordinates using the Lagrange multiplier technique. Then the velocity transformation matrix is used to derive a minimum number of equations of motion in terms of a set of independent joint coordinates. An illustrative example and numerical results are presented, and the advantages and disadvantages of the method are discussed.

Instant Center Based Kinematic Formulation for Planar Wheeled Platforms

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Amit Kulkarni ◽  
Delbert Tesar
Keyword(s):  
Rigid Body ◽  
Input Parameter ◽  
Radial Distance ◽  
Planar Motion ◽  
Mobile Platform ◽  
General Point ◽  
Kinematic Modeling ◽  
Mobile Platforms ◽  
General Order ◽  
Operational Criteria

For a general J wheeled mobile platform capable of up to three-degrees-of-freedom planar motion, there are up to two J independent input parameters yet the output of the platform is completely represented by three independent variables. This leads to an input parameter resolution problem based on operational criteria, which are in development just as they have been developed for n input manipulator systems. To resolve these inputs into a meaningful decision structure means that all motions at the wheel attachment points must have clear physical meaning. To this effect, we propose a methodology for kinematic modeling of multiwheeled mobile platforms using instant centers to efficiently describe the motion of all system points up to the nth order using a generalized algebraic formulation. This is achieved by using a series of instant centers (velocity, acceleration, jerk, and jerk derivative), where each point in the system has a motion property with its magnitude proportional to the radial distance of the point from the associated instant center and at a constant angle relative to that radius. The method of instant center provides a straightforward and physically intuitive way to synthesize a general order planar motion of mobile platforms. It is shown that a general order motion property of any point on a rigid body follows two properties, namely, directionality and proportionality, with respect to the corresponding instant center. The formulation presents a concise expression for a general order motion property of a general point on the rigid body with the magnitude and direction separated and identified. The results are summarized for up to the fifth order motion in the summary table. Based on the initial formulation, we propose the development of operational criteria using higher order properties to efficiently synthesize the motion of a J wheeled mobile platform.

Global dynamical time for binary point-like particle systems

2020 ◽  
Vol 17 (09) ◽  
pp. 2050131
Author(s):  
Osvaldo M. Moreschi
Keyword(s):  
Equations Of Motion ◽  
Minkowski Spacetime ◽  
Particle Systems ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Retarded Time ◽  
Dynamical Time ◽  
The Difference ◽  
Multiple Particle ◽  
Equations Of Motions

A geometrical construction for a global dynamical time for binary point-like particle systems, modeled by relativistic equations of motions, is presented. Thus, we provide a convenient tool for the calculation of the dynamics of recent models for the dynamics of black holes that use individual proper times. The construction is naturally based on the local Lorentzian geometry of the spacetime considered. Although in this presentation we are dealing with the Minkowskian spacetime, the construction is useful for gravitational models that have as a seed Minkowski spacetime. We present the discussion for a binary system, but the construction is obviously generalizable to multiple particle systems. The calculations are organized in terms of the order of the corresponding relativistic forces. In particular, we improve on the Darwin and Landau–Lifshitz approaches, for the case of electromagnetic systems. We discuss the possibility of a Lagrangian treatment of the retarded effects, depending on the nature of the relativistic forces. The higher-order contractions are based on a Runge–Kutta type procedure, which is used to calculate the quantities at the required retarded time, by increasing evaluations of the forces at intermediate times. We emphasize the difference between approximation orders in field equations and approximation orders in retarded effects in the equations of motion. We show this difference by applying our construction to the binary electromagnetic case.

scholarly journals Analytical Calculation of Power Flow in Three Coupled Oscillators and its Application to One Dimensional Crystal

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Chifu Ebene Ndikilar ◽  
Sofwan I. Saleh ◽  
Hafeez Yusuf Hafeez ◽  
Lawan Sani Taura
Keyword(s):  
White Noise ◽  
Coupled Oscillators ◽  
Power Flow ◽  
Equations Of Motion ◽  
Analytical Calculation ◽  
Asymptotic Value ◽  
One Dimensional ◽  
Two Systems ◽  
Dimensional Crystal ◽  
Equations Of Motions

The motion of a system consisting of three coupled oscillators of three masses attached together by four springs is studied analytically. The system is used as a model to describe the interactions between atoms in a one dimensional crystal with spring-like forces under white noise excitations.  Two different cases are considered and the frequencies of oscillations are obtained as well as the equations of motion.  The equations of motions are used to determine the power flow in the systems. The power flow determined is used to describe the effects of substitution impurities in a crystal. The power flow of the two systems studied decreases exponentially with increase in frequency to an asymptotic value.

Mobile Computing: The Next Platform Rivalry

2014 ◽  
Vol 104 (5) ◽  
pp. 475-480 ◽  
Author(s):  
Timothy Bresnahan ◽  
Shane Greenstein
Keyword(s):  
Mobile Computing ◽  
Mobile Platform ◽  
Mobile Platforms ◽  
Platform Governance ◽  
Hierarchical Governance ◽  
The Way

Competition to become one of several dominant mobile platforms is intense. Platforms compete for developers, who create applications which make the platform valuable for users. Why doesn't one form of platform governance emerge as superior? This essay will stress the reasons for differentiation and proposes a new argument linked to a platform's “hierarchy.” Hierarchical governance features can help at one moment but then get in the way at a later time. These arguments are illustrated by different approaches to platform governance taken by the major mobile platform sponsors of recent years.

CFD Approach to Modelling Hydrodynamic Characteristics of Underwater Glider

2019 ◽  
Vol 2019 (4) ◽  
pp. 32-45
Author(s):  
Kamila Stryczniewicz ◽  
Przemysław Drężek
Keyword(s):  
Flow Behavior ◽  
Equations Of Motion ◽  
Vertical Plane ◽  
Dynamic Modelling ◽  
The Body ◽  
Hydrodynamic Characteristics ◽  
Motion Simulation ◽  
Underwater Glider ◽  
Lift And Drag ◽  
Equations Of Motions

Abstract Autonomous underwater gliders are buoyancy propelled vehicles. Their way of propulsion relies upon changing their buoyancy with internal pumping systems enabling them up and down motions, and their forward gliding motions are generated by hydrodynamic lift forces exerted on a pair of wings attached to a glider hull. In this study lift and drag characteristics of a glider were performed using Computational Fluid Dynamics (CFD) approach and results were compared with the literature. Flow behavior, lift and drag forces distribution at different angles of attack were studied for Reynolds numbers varying around 105 for NACA0012 wing configurations. The variable of the glider was the angle of attack, the velocity was constant. Flow velocity was 0.5 m/s and angle of the body varying from −8° to 8° in steps of 2°. Results from the CFD constituted the basis for the calculation the equations of motions of glider in the vertical plane. Therefore, vehicle motion simulation was achieved through numeric integration of the equations of motion. The equations of motions will be solved in the MatLab software. This work will contribute to dynamic modelling and three-dimensional motion simulation of a torpedo shaped underwater glider.

Orientation Workspace Analysis of 6-DOF Parallel Manipulators

1999 ◽  
Author(s):  
Ilian A. Bonev ◽  
Jeha Ryu
Keyword(s):  
Fixed Point ◽  
Direct Method ◽  
Parallel Manipulators ◽  
Mobile Platform ◽  
Euler Angles ◽  
Discretization Method ◽  
Workspace Analysis ◽  
A Direct Method ◽  
Orientation Workspace

Abstract This paper presents a new discretization method for the computation of the orientation workspace of 6-rDOF parallel manipulators, defined as the set of all attainable orientations of the mobile platform about a fixed point. The method is based on the use of a modified set of Euler angles and a particular representation of the orientation workspace. In addition, a direct method is suggested for the computation of the projected orientation workspace, defined as the set of all possible directions of the approach vector of the mobile platform. Alternative ways of computing these two types of workspaces are also discussed with typical examples.

Stochastic Equations Of Motion

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Time Evolution ◽  
Stochastic Dynamics ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Stochastic Equations ◽  
The State ◽  
Stochastic Variable ◽  
Stochastic Nature ◽  
Full Phase Space ◽  
Equations Of Motions

We have already observed that the full phase space description of a system of N particles (taking all 6N coordinates and velocities into account) requires the solution of the deterministic Newton (or Schrödinger) equations of motion, while the time evolution of a small subsystem is stochastic in nature. Focusing on the latter, we would like to derive or construct appropriate equations of motion that will describe this stochastic motion. This chapter discusses some methodologies used for this purpose, focusing on classical mechanics as the underlying dynamical theory. In Chapter 10 we will address similar issues in quantum mechanics. The time evolution of stochastic processes can be described in two ways: 1. Time evolution in probability space. In this approach we seek an equation (or equations) for the time evolution of relevant probability distributions. In the most general case we deal with an infinite hierarchy of functions, P(zntn; zn−1tn−1; . . . ; z1t1) as discussed in Section 7.4.1, but simpler cases exist, for example, for Markov processes the evolution of a single function, P(z, t; z0t0), fully characterizes the stochastic dynamics. Note that the stochastic variable z stands in general for all the variables that determine the state of our system. 2. Time evolution in variable space. In this approach we seek an equation of motion that describes the evolution of the stochastic variable z(t) itself (or equations of motion for several such variables). Such equations of motions will yield stochastic trajectories z(t) that are realizations of the stochastic process under study. The stochastic nature of these equations is expressed by the fact that for any initial condition z0 at t = t0 they yield infinitely many such realizations in the same way that measurements of z(t) in the laboratory will yield different such realizations. Two routes can be taken to obtain such stochastic equations of motions, of either kind: 1. Derive such equations from first principles. In this approach, we start with the deterministic equations of motion for the entire system, and derive equations of motion for the subsystem of interest. The stochastic nature of the latter stems from the fact that the state of the complementary system, “the rest of the world,” is not known precisely, and is given only in probabilistic terms.

Mobile Platforms and Multi-Mobile Platform Development

2014 ◽  
Vol 21 (4) ◽  
pp. 529-552 ◽  
Author(s):  
Hassan Charaf ◽  
Péter Ekler ◽  
Tamás Mészáros ◽  
Imre Kelényi ◽  
Bence Kovari ◽  
...  
Keyword(s):  
Mobile Platform ◽  
Mobile Platforms ◽  
Platform Development

Workspace analysis and design of large-scale cable-driven printing robot considering cable mass and mobile platform orientation

2021 ◽  
Vol 165 ◽  
pp. 104426
Author(s):  
Ishan Chawla ◽  
P.M. Pathak ◽  
Leila Notash ◽  
A.K. Samantaray ◽  
Qingguo Li ◽  
...  
Keyword(s):  
Large Scale ◽  
Mobile Platform ◽  
Analysis And Design ◽  
Workspace Analysis
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