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.

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.

The Research on Rake-Car’s Driving System of Ore Reclaimer

2013 ◽  
Vol 300-301 ◽  
pp. 10-13
Author(s):  
Yuan Hui Li ◽  
Kui Sheng Chen ◽  
Jiang Hong Deng ◽  
Xin Yuan Chen
Keyword(s):  
Computer Simulation ◽  
System Design ◽  
Failure Rate ◽  
Hydraulic System ◽  
Driving Mechanism ◽  
Connecting Rod ◽  
Driving System ◽  
Final Design ◽  
Hydraulic System Design ◽  
Working Situation

Rake-car’s driving system of ore reclaimer originally used crank and connecting rod mechanism as driving mechanism. The driving mechanism got some trouble that parts got severe wear and failure rate of mechanism was high. The hydraulic system is used to drive rake car in view of hydraulic driving system’s advantage. By analysis on existing problem of crank and connecting rod mechanism, the actual working load of equipment is tested and the working situation is analysed. The working situation of the hydraulic system is also analysed by computer simulation. By optimization of the hydraulic system design, the final design is determined. The whole system is actually used. It works well.

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.

scholarly journals Large Evaporite Provinces: Geothermal rather than Solar Origin?

2020 ◽  
Author(s):  
Zhanjie Qin ◽  
Chunan Tang ◽  
Xiying Zhang ◽  
Tiantian Chen ◽  
Xiangjun Liu ◽  
...  
Keyword(s):  
Large Scale ◽  
Climatic Factors ◽  
Temporal Distribution ◽  
Tectonic Activity ◽  
Driving Mechanism ◽  
Solar Origin ◽  
Tectonically Active ◽  
Spatio Temporal ◽  
Thermal Influence ◽  
The Masses

Abstract Large evaporite provinces (LEPs) represent prodigious volumes of evaporites widely developed from the Sinian to Neogene. The reasons why they often quickly develop on a large scale with large areas and thicknesses remain enigmatic. Possible causes range from warming from above to heating from below. The fact that the salt deposits in most salt-bearing basins occur mainly in the Sinian-Cambrian, Permian-Triassic, Jurassic-Cretaceous, and Miocene intervals favours a dominantly tectonic origin rather than a solar driving mechanism. Here, we analysed the spatio-temporal distribution of evaporites based on 138 evaporitic basins and found that throughout the Phanerozoiceon, LEPs occurred across the Earth’s surface in most salt-bearing basins, especially in areas with an evolutionary history of strong tectonic activity. The masses of evaporites, rates of evaporite formation, tectonic movements, and large igneous provinces (LIPs) synergistically developed in the Sinian-Cambrian, Permian, Jurassic-Cretaceous, and Miocene intervals, which are considered to be four of the warmest times since the Sinian. We realize that salt accumulation can proceed without solar energy and can generally be linked to geothermal changes in tectonically active zones. When climatic factors are involved, they may be manifestations of the thermal influence of the crust on the surface.

scholarly journals Modeling a Knuckle-Boom Crane Control to Reduce Pendulum Motion Using the Moving Frame Method

2019 ◽  
Author(s):  
Maren Eriksen Eia ◽  
Elise Mari Vigre ◽  
Thorstein Ravneberg Rykkje
Keyword(s):  
Equations Of Motion ◽  
Moving Frame ◽  
Web Pages ◽  
Moving Frames ◽  
Pendulum Motion ◽  
Moving Frame Method ◽  
Frame Method ◽  
The Masses ◽  
And Control ◽  
Boom Crane

Abstract A Knuckle Boom Crane is a pedestal-mounted, slew-bearing crane with a joint in the middle of the distal arm; i.e. boom. This distal boom articulates at the ‘knuckle (i.e.: joint)’ and that allows it to fold back like a finger. This is an ideal configuration for a crane on a ship where storage space is a premium. This project researches the motion and control of a ship mounted knuckle boom crane to minimize the pendulum motion of a hanging load. To do this, the project leverages the Moving Frame Method (MFM). The MFM draws upon Lie group theory — SO(3) and SE(3) — and Cartan’s Moving Frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. The work reported here accounts for the masses and geometry of all components, interactive motor couples and prepares for buoyancy forces and added mass on the ship. The equations of motion are solved numerically using a 4th order Runge Kutta (RK4), while solving for the rotation matrix for the ship using the Cayley-Hamilton theorem and Rodriguez’s formula for each timestep. This work displays the motion on 3D web pages, viewable on mobile devices.

Consequences of compliant walls for peristaltic transportation in a channel having porous medium and porous boundaries

2019 ◽  
Vol 97 (6) ◽  
pp. 599-608 ◽  
Author(s):  
Iqra Shahzadi ◽  
S. Nadeem
Keyword(s):  
Porous Medium ◽  
Distribution Function ◽  
Velocity Distribution ◽  
Amplitude Ratio ◽  
Equations Of Motion ◽  
Velocity Distribution Function ◽  
Driving Mechanism ◽  
Regular Perturbation ◽  
Mean Velocity ◽  
Porous Boundaries

The current communication addresses the two-dimensional peristaltic transport of viscous fluid in a channel having porous medium as well as porous boundaries. The walls of the channel are assumed to be compliant to represent the driving mechanism of the muscle. The equations of motion are considered for the deformable boundaries and the fluid to investigate the fluid–solid interaction problem. The zeroth-, first-, and second-order solutions of stream function for a small amplitude ratio are determined by using regular perturbation. Impact of related parameters on quantities D1, D2, mean velocity perturbation function, and mean velocity distribution function are interpreted graphically. One fundamental finding of the considered examination is that the increase in permeability parameter increases the amplitude of the velocity distribution function.

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.

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.

Modelling Buoy Motion at Sea

2019 ◽  
Author(s):  
Thorstein R. Rykkje ◽  
Tord Tørressen ◽  
Håvard Løkkebø
Keyword(s):  
Equations Of Motion ◽  
Moving Frame ◽  
Web Pages ◽  
Moving Frames ◽  
Lie Group Theory ◽  
Moving Frame Method ◽  
Frame Method ◽  
And Mathematics ◽  
The Masses ◽  
Theoretical Results

Abstract This project creates a model to assess the motion induced on a buoy at sea, under wave conditions. We use the Moving Frame Method (MFM) to conduct the analysis. The MFM draws upon concepts and mathematics from Lie group theory — SO(3) and SE(3) — and Cartan’s notion of Moving Frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. This work accounts for the masses and geometry of all components and for buoyancy forces and added mass. The resulting movement will be displayed on 3D web pages using WebGL. Finally, the theoretical results will be compared with experimental data obtained from a previous project done in the wave tank at HVL.

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