A Novel Method to Model the Dynamics of an Uniball Robot

2014 ◽  
Author(s):  
Pramod Chembrammel ◽  
Thenkurussi Kesavadas
Keyword(s):  
Fixed Point ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Euler Method ◽  
Kinematics And Dynamics ◽  
Euler Angles ◽  
Geometrical Center ◽  
Principal Moments Of Inertia ◽  
Geometrical Features ◽  
Novel Method

In this paper the kinematics and dynamics of a uniball robot is demonstrated. The motion of a uniball robot is derived from the dynamics of a sphere rolling on a surface which is considered as a motion about a fixed point. The equations of motion are derived using Newton-Euler method incorporating the geometrical features of the surface. A uniball-robot can be considered as a Routh’s sphere whose center of mass is not at the geometrical center and have equal principal moments of inertia in the plane perpendicular to the axis connecting the center of mass and the geometrical center. The Euler angles are obtained using the Meusnier’s theorem which deals with the evolution of the surface as the robot moves along.

Design of a Spherical Robot With Cable-Actuated Driving Mechanism

2017 ◽  
Author(s):  
Ernur Karadoğan ◽  
Brian P. DeJong
Keyword(s):  
Equations Of Motion ◽  
Center Of Mass ◽  
Kinematics And Dynamics ◽  
Driving Mechanism ◽  
Moving Mass ◽  
Spherical Robot ◽  
Driving System ◽  
Dynamic Mass ◽  
Rolling Torque ◽  
The Masses

This paper presents the kinematics and dynamics of a spherical robot with a mechanical driving system that consists of four cable-actuated moving masses. Four cable-pulley systems control four tetrahedrally-located movable masses and the robot functions by shifting its center of mass to create rolling torque. The cable actuation decreases overall mass and, therefore, allow for less energy expenditure, as compared to other moving mass mechanisms that translate the masses by powered-screws. Additionally, the design allows the center of mass for the static (spherical shell, electronics, motors etc.) and dynamic mass (moving masses) to be at the geometric center at any given time, therefore has potential for tumbleweeding when needed. The derived equations of motion are verified by means of simulations.

scholarly journals The Stability Conditions for a Heavy Solid Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
A. I. Ismail
Keyword(s):  
Equations Of Motion ◽  
Center Of Mass ◽  
Sufficient Conditions ◽  
The Body ◽  
Stability Conditions ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Necessary And Sufficient

In this paper, the stability conditions for the rotary motion of a heavy solid about its fixed point are considered. The center of mass of the body is assumed to lie on the moving z-axis which is assumed to be the minor axis of the ellipsoid of inertia. The nonlinear equations of motion and their three first integrals are obtained when the principal moments of inertia are distributed as I 1 < I 2 < I 3 . We construct a Lyapunov function L to investigate the stability conditions for this motion. We give a numerical example to illustrate the necessary and sufficient conditions for the stability of the body at certain moments of inertia. This problem has many important applications in different sciences.

scholarly journals Dynamics of Space Particles and Spacecrafts Passing by the Atmosphere of the Earth

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vivian Martins Gomes ◽  
Antonio Fernando Bertachini de Almeida Prado ◽  
Justyna Golebiewska
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
The Sun ◽  
Three Body Problem ◽  
The Earth ◽  
Before And After ◽  
Three Body ◽  
Body Energy ◽  
Spacecraft Position

The present research studies the motion of a particle or a spacecraft that comes from an orbit around the Sun, which can be elliptic or hyperbolic, and that makes a passage close enough to the Earth such that it crosses its atmosphere. The idea is to measure the Sun-particle two-body energy before and after this passage in order to verify its variation as a function of the periapsis distance, angle of approach, and velocity at the periapsis of the particle. The full system is formed by the Sun, the Earth, and the particle or the spacecraft. The Sun and the Earth are in circular orbits around their center of mass and the motion is planar for all the bodies involved. The equations of motion consider the restricted circular planar three-body problem with the addition of the atmospheric drag. The initial conditions of the particle or spacecraft (position and velocity) are given at the periapsis of its trajectory around the Earth.

GPR-based novel approach for non-linear aerodynamic modelling from flight data

2018 ◽  
Vol 123 (1259) ◽  
pp. 79-92
Author(s):  
A. Kumar ◽  
A. K. Ghosh
Keyword(s):  
Aerodynamic Force ◽  
Equations Of Motion ◽  
Gaussian Process Regression ◽  
Likelihood Estimation ◽  
Flight Data ◽  
Novel Approach ◽  
Non Linear ◽  
Research Aircraft ◽  
Novel Method ◽  
Aerodynamic Modelling

ABSTRACTIn this paper, a Gaussian process regression (GPR)-based novel method is proposed for non-linear aerodynamic modelling of the aircraft using flight data. This data-driven regression approach uses the kernel-based probabilistic model to predict the non-linearity. The efficacy of this method is examined and validated by estimating force and moment coefficients using research aircraft flight data. Estimated coefficients of aerodynamic force and moment using GPR method are compared with the estimated coefficients using maximum-likelihood estimation (MLE) method. Estimated coefficients from the GPR method are statistically analysed and found to be at par with estimated coefficients from MLE, which is popularly used as a conventional method. GPR approach does not require to solve the complex equations of motion. GPR further can be directed for the generalised applications in the area of aeroelasticity, load estimation, and optimisation.

scholarly journals Obstacle Detection in Cluttered Traffic Environment Based on Candidate Generation and Classification

2006 ◽  
Vol 1 (4) ◽  
pp. 93 ◽  
Author(s):  
Qing Li ◽  
F.C. Sun
Keyword(s):  
Vehicle Detection ◽  
Obstacle Detection ◽  
Experimental Results ◽  
Geometrical Features ◽  
Traffic Environment ◽  
Novel Method ◽  
Shadow Cast

A novel method to detect vehicles is presented in the paper. Assumption of the vehicle is made using the geometrical features of the vehicle rear by the statistical histogram. Then hypothesis is verified using the property of the shadow cast by the car according to a prior acknowledgement of traffic scene. Finally, the vehicle detection is realized by hypothesis and verification of objects. The experimental results show the efficiency and feasibility of the method.

Multibody Dynamics on Differentiable Manifolds

2021 ◽  
Vol 16 (4) ◽  
Author(s):  
Edward J. Haug
Keyword(s):  
Euclidean Space ◽  
Differential Equations ◽  
Vector Space ◽  
Ordinary Differential Equations ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differentiable Manifold ◽  
Kinematics And Dynamics ◽  
Variational Equations ◽  
Differentiable Manifolds

Abstract Topological and vector space attributes of Euclidean space are consolidated from the mathematical literature and employed to create a differentiable manifold structure for holonomic multibody kinematics and dynamics. Using vector space properties of Euclidean space and multivariable calculus, a local kinematic parameterization is presented that establishes the regular configuration space of a multibody system as a differentiable manifold. Topological properties of Euclidean space show that this manifold is naturally partitioned into disjoint, maximal, path connected, singularity free domains of kinematic and dynamic functionality. Using the manifold parameterization, the d'Alembert variational equations of multibody dynamics yield well-posed ordinary differential equations of motion on these domains, without introducing Lagrange multipliers. Solutions of the differential equations satisfy configuration, velocity, and acceleration constraint equations and the variational equations of dynamics, i.e., multibody kinematics and dynamics are embedded in these ordinary differential equations. Two examples, one planar and one spatial, are treated using the formulation presented. Solutions obtained are shown to satisfy all three forms of kinematic constraint to within specified error tolerances, using fourth-order Runge–Kutta numerical integration methods.

Development of Equations of Motion for a Stewart Platform Under Prescribed Mount Motion

2018 ◽  
Author(s):  
Takeyuki Ono ◽  
Ryosuke Eto ◽  
Junya Yamakawa ◽  
Hidenori Murakami
Keyword(s):  
Rigid Body ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Base Plate ◽  
Stewart Platform ◽  
Euler Method ◽  
Moving Frame ◽  
Real Time Control ◽  
Precise Positioning ◽  
Time Control

Analytical equations of motion are critical for real-time control of translating manipulators, which require precise positioning of various tools for their mission. Specifically, when manipulators mounted on moving robots or vehicles perform precise positioning of their tools, it becomes economical to develop a Stewart platform, whose sole task is stabilizing the orientation and crude position of its top table, onto which various precision tools are attached. In this paper, analytical equations of motion are developed for a Stewart platform whose motion of the base plate is prescribed. To describe the kinematics of the platform, the moving frame method, presented by one of authors [1,2], is employed. In the method the coordinates of the origin of a body attached coordinate system and vector basis are expressed by using 4 × 4 frame connection matrices, which form the special Euclidean group, SE(3). The use of SE(3) allows accurate description of kinematics of each rigid body using (relative) joint coordinates. In kinetics, the principle of virtual work is employed, in which system virtual displacements are expressed through B-matrix by essential virtual displacements, reflecting the connection of the rigid body system [2]. The resulting equations for fixed base plate reduce to those for the top plate, obtained by the Newton-Euler method. A main result of the paper is the analytical equations of motion in matrix form for dynamics analyses of a Stewart platform whose base plate moves. The control applications of those equations will be deferred to subsequent publications.

RUNNING PATTERN GENERATION OF HUMANOID BIPED WITH A FIXED POINT AND ITS REALIZATION

2009 ◽  
Vol 06 (04) ◽  
pp. 631-656 ◽  
Author(s):  
BAEK-KYU CHO ◽  
ILL-WOO PARK ◽  
JUN-HO OH
Keyword(s):  
Fixed Point ◽  
Angular Momentum ◽  
Sagittal Plane ◽  
Center Of Mass ◽  
Maximum Velocity ◽  
Frontal Plane ◽  
Numerical Approach ◽  
Pattern Generation ◽  
Upper Body ◽  
Running Pattern

This paper discusses the generation of a running pattern for a humanoid biped and verifies the validity of the proposed method of running pattern generation via experiments. Two running patterns are generated independently in the sagittal plane and in the frontal plane and the two patterns are then combined. When a running pattern is created with resolved momentum control in the sagittal plane, the angular momentum of the robot about the Center of Mass (COM) is set to zero, as the angular momentum causes the robot to rotate. However, this also induces unnatural motion of the upper body of the robot. To solve this problem, the biped was set as a virtual under-actuated robot with a free joint at its support ankle, and a fixed point for a virtual under-actuated system was determined. Following this, a periodic running pattern in the sagittal plane was formulated using the fixed point. The fixed point is easily determined in a numerical approach. In this way, a running pattern in the frontal plane was also generated. In an experiment, a humanoid biped known as KHR-2 ran forward using the proposed running pattern generation method. Its maximum velocity was 2.88 km/h.

AN ACTION PRINCIPLE FOR MAGNETOHYDRODYNAMICS

1963 ◽  
Vol 41 (12) ◽  
pp. 2241-2251 ◽  
Author(s):  
M. G. Calkin
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Magnetic Induction ◽  
Vector Potential ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Action Principle ◽  
Invariance Properties ◽  
Conservation Of Momentum

The equations of motion of an inviscid, infinitely conducting fluid in an electromagnetic field are transformed into a form suitable for an action principle. An action principle from which these equations may be derived is found. The conservation laws follow from invariance properties of the action. The space–time invariances lead to the conservation of momentum, energy, angular momentum, and center of mass, while the gauge invariances lead to conservation of mass, a generalization of the Helmholtz vortex theorem of hydrodyanmics, and the conservation of the volume integrals of A∙B and v∙B, where A is the vector potential, B is the magnetic induction, and v is the fluid velocity.

A New Finding on the Dynamic Stiffness Matrices of Asymmetric and Axisymmetric Shafts

2001 ◽  
Author(s):  
Francesco A. Raffa ◽  
Furio Vatta
Keyword(s):  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Rotational Inertia ◽  
Dynamic Stiffness Matrix ◽  
Rayleigh Beam ◽  
Principal Moments Of Inertia ◽  
Stiffness Matrices ◽  
New Finding

Abstract In this paper the dynamic stiffness method is developed to analyze a rotating asymmetric shaft, i.e. a shaft whose transverse section is characterized by dissimilar principal moments of inertia. The shaft is modeled according to the Rayleigh beam theory including the effects of both translational and rotational inertia, and gyroscopic moments. The mathematical description is carried out in a reference system rotating at the shaft speed and is based on the exact solution of the governing differential equations of motion. The exact expressions of the shaft displacements are utilized for deriving the 8 × 8 complex dynamic stiffness matrix of the shaft. A new relationship is obtained which links the dynamic stiffness matrix of the asymmetric shaft to the 4 × 4 real dynamic stiffness matrix of the axisymmetric shaft.

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