Forward and Inverse Displacement Analysis of an Actuated Spoke Wheel Robot With Two Spokes and a Tail Contact With the Ground

2010 ◽  
Author(s):  
Ping Ren ◽  
Dennis Hong
Keyword(s):  
Design Optimization ◽  
Ground Motion ◽  
Numerical Solutions ◽  
Convex Surface ◽  
Polynomial Equations ◽  
Surface Geometry ◽  
Displacement Analysis ◽  
Unstructured Environments ◽  
Straight Line ◽  
Rigid Shell

Intelligent Mobility Platform with Active Spoke System (IMPASS) is a unique wheel-leg hybrid robot that can walk in unstructured environments by stretching in or out three independently actuated spokes of each wheel. The latest prototype of IMPASS has two actuated spoke wheels and one passive tail. In order to maintain its stability, the tail of the robot is designed as a rigid shell with a geometrically convex surface touching the ground. IMPASS is considered as a mechanism with variable topologies (MVTs) due to its metamorphic configurations. Its motions on the ground, such as steering, straight-line walking and other combinations, can be uniformly interpreted as a series of configuration transformations. Among all cases of its topologies, the cases with two spokes and the tail in contact with the ground possess two d.o.f and contribute the most to its ground motion. To fully understand the characteristics of such topologies, the forward and inverse displacement analysis is developed for these cases, with the polynomial equations derived. Numerical solutions from simulation are present to validate their formulation. These results lay the kinematics foundation for the motion monitoring and planning of IMPASS. It also contributes to the design optimization of the tail’s surface geometry to improve its adaptability on uneven terrains.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

An n-Vertex Theorem for Convex Space Curves

1985 ◽  
Vol 37 (2) ◽  
pp. 217-237
Author(s):  
Tibor Bisztriczky
Keyword(s):  
Topological Space ◽  
Euclidean Plane ◽  
Convex Surface ◽  
Space Curves ◽  
Straight Line ◽  
History Of ◽  
General Convex ◽  
Vertex Theorem ◽  
The Subject ◽  
Three Space

The classical four-vertex theorem states that a simple closed convex C2 curve in the Euclidean plane has at least four vertices (points of extreme curvature). This theorem has many generalizations with regard to both the curve and the topological space and for a history of the subject, we refer to [4] and [1]. The particular generalization of concern, credited to H. Mohrmann, is the following n-vertex theorem.Let a simple closed C3 curve on a closed convex surface be intersected by a suitable plane in n points. Then the curve has at least n inflections (vertices).The closed convex surface in the preceding is defined as having at most two points in common with any straight line. Presently, we extend this result to curves on more general convex surfaces in a real projective three-space P3.

Numerical Solutions of Polynomial Equations for the Eight-Position Synthesis of the Cylindrical-Spherical Dyad

2012 ◽  
Author(s):  
Chintien Huang ◽  
Chenning Hung ◽  
Kuenming Tien
Keyword(s):  
Rigid Body ◽  
Numerical Solutions ◽  
Continuation Method ◽  
Quadratic Equation ◽  
Geometric Constraints ◽  
Numerical Continuation ◽  
Polynomial Equations ◽  
Quartic Polynomial ◽  
Solutions Of Equations ◽  
Position Synthesis

This paper investigates the numerical solutions of equations for the eight-position rigid-body guidance of the cylindrical-spherical (C-S) dyad. We seek to determine the number of finite solutions by using the numerical continuation method. We derive the design equations using the geometric constraints of the C-S dyad and obtain seven quartic polynomial equations and one quadratic equation. We then solve the system of equations by using the software package Bertini. After examining various specifications, including those with random complex numbers, we conclude that there are 804 finite solutions of the C-S dyad for guiding a body through eight prescribed positions. When designing spatial dyads for rigid-body guidance, the C-S dyad is one of the four dyads that result in systems of equal numbers of equations and unknowns if the maximum number of allowable positions is specified. The numbers of finite solutions in the syntheses of the other three dyads have been obtained previously, and this paper provides the computational kinematic result of the last unsolved problem, the eight-position synthesis of the C-S dyad.

Numerical Simulation of a Slipper Model for Swash Plate Type Axial Piston Pumps and Motors: Effects of Concave and Convex Surface Geometry

2012 ◽  
Vol 6 (4) ◽  
pp. 434-439 ◽  
Author(s):  
Toshiharu Kazama ◽  
◽  
Yukihito Narita
Keyword(s):  
Convex Surface ◽  
Sliding Surface ◽  
Surface Geometry ◽  
Axial Piston Pumps ◽  
Swash Plate ◽  
Convex Geometries ◽  
Thrust Pad ◽  
Axial Piston ◽  
Plate Type ◽  
Load Conditions

In this study, the slipper of swash plate axial piston pumps and motors is modeled as a hybrid (hydrostatic and hydrodynamic) thrust pad bearing. The effects of the slightly concave and convex geometries of the slipper sliding surface are examined. The motion of the slipper model is numerically simulated, and its tribological characteristics are examined under eccentric and dynamic load conditions. The calculations under these conditions indicate that, for the concave slipper, the fluctuation of the bearing pad azimuth increases, and the attitude of the slipper becomes unstable. In contrast, for the convex slipper, the attitude becomes stable, but the clearance increases.

Design Optimization of Circumferential Casing Grooves for a Transonic Axial Compressor to Enhance Stall Margin

2010 ◽  
Author(s):  
Kwang-Jin Choi ◽  
Jin-Hyuk Kim ◽  
Kwang-Yong Kim
Keyword(s):  
Design Optimization ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Latin Hypercube Sampling ◽  
Optimum Shape ◽  
Data Set ◽  
Stall Margin

This paper presents a design optimization of an axial compressor with NASA Rotor 37 and five circumferential casing grooves for enhancement of stall margin. Three-dimensional Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence model are discretized by finite volume approximations and solved on hexahedral grids for the flow analyses. The validation of the numerical results is performed in comparison with experimental data for pressure ratio and adiabatic efficiency. The Latin-hypercube sampling as design-of-experiments is used to generate the twelve design points within the design space. A stall margin parameter is considered as an objective function with two design variables defining the geometry of the circumferential casing grooves. The radial basis neural network method employed as a surrogate model for the design optimization of the circumferential casing grooves is trained on the numerical solutions by carrying out leave-one-out cross-validation for the data set. The results show that the stall margin of the optimum shape is enhanced considerably by the design optimization compared to the cases with smooth casing and the reference grooves.

NUMERICAL SOLUTIONS OF POLYNOMIAL EQUATIONS

1968 ◽  
Author(s):  
Tadeusz Leser ◽  
Henry Wisniewski
Keyword(s):  
Numerical Solutions ◽  
Polynomial Equations

Density of decompression bubbles and competition for gas among bubbles, tissue, and blood

1993 ◽  
Vol 75 (5) ◽  
pp. 2293-2301 ◽  
Author(s):  
H. D. Van Liew ◽  
M. E. Burkard
Keyword(s):  
Partial Pressure ◽  
Time Course ◽  
Numerical Solutions ◽  
Bubble Formation ◽  
Total System ◽  
Dissolved Gas ◽  
Low Level ◽  
Straight Line ◽  
The Many

We used numerical solutions of a system of equations to simulate gas exchanges of bubbles after a decompression, with particular attention to the effect of number of bubble formation sites per unit of tissue. If many bubbles grow, they deplete the excess dissolved gas in the tissue. The consequences are as follows: 1) the many individual bubbles do not become as large as they would if fewer were competing for gas; 2) more gas is evolved when there are many sites; 3) the bubbles are absorbed sooner than the bigger bubbles that grow with few sites; 4) after diffusion into many bubbles causes N2 partial pressure in the tissue to fall immediately to a low level, N2 partial pressure in the tissue and the exiting blood remain "clamped" to this low level because dissolved N2 removed by blood is replenished by diffusion out of the bubbles; and 5) as long as many bubbles persist, the long-term removal of inert gas from the total system (tissue plus bubbles) follows a straight-line time course rather than an exponential course.

Numerical Simulation of Roller Hemming Operation on Convex Edge-Convex Surface Parts

2016 ◽  
Vol 15 ◽  
pp. 75-84 ◽  
Author(s):  
Selim Gürgen
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Sheet Metal ◽  
Process Parameters ◽  
Convex Surface ◽  
Visual Quality ◽  
Surface Geometry ◽  
Bending Angle

This paper presents the roller hemming operation of FEE220BH sheet metal with convex edge-convex surface geometry. The investigation is focused on process parameters of bending angle and roller geometry whose effects have not been investigated in previous studies. A set of numerical simulations is designed to observe the multi response of the process parameters. The objective of the study is to determine the influences of these parameters on deformation, undesired wrinkling formation and hemming force which are directly related to the material reliability and the visual quality in the operation. The results are discussed to improve the outputs of the operation.

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