Closed-Form Solutions to the Spherical Joint Attachment Problem

1992 ◽  
Vol 114 (2) ◽  
pp. 269-273 ◽  
Author(s):  
M. M. Stanisˇic´ ◽  
K. C. Gupta
Keyword(s):  
Closed Form ◽  
Eigenvalue Problems ◽  
Surface Fitting ◽  
Central Axis ◽  
Opening Angle ◽  
Spherical Joint ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Axis Of Symmetry ◽  
Fitting Problem

This paper presents closed-form solutions to the problem of defining the attachment of a spherical joint (a ball and socket) in a spatial linkage. The defined attachment should minimize the opening angle of the socket, maximizing the ball retention capability. Previous solutions to this problem have used iterative searching techniques, which are computationally intense. In this paper the problem is reformulated as a surface fitting problem. Two formulations are presented, both of which require the solution of the associated eigenvalue problems. The eigenvectors correspond to the central axis of symmetry for the socket opening. A numerical example is presented to compare the results obtained by these formulations with those available in the literature.

Kinematics of a n–bay triangle–triangle variable geometry truss manipulator

Robotica ◽  
1992 ◽  
Vol 10 (3) ◽  
pp. 263-267
Author(s):  
L. Beiner
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Variable Length ◽  
Variable Geometry ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Forward And Inverse Kinematics ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

SUMMARYVariable geometry truss manipulators (VGTM) are static trusses where the lengths of some members can be varied, allowing one to control the position of the free end relative to the fixed one. This paper deals with a planar VGTM consisting of a n–bay triangle-triangle truss with one variable length link (i.e. one DOF) per bay. Closed-form solutions to the forward, inverse, and velocity kinematics of a 3-DOF version of this VGTM are presented, while the forward and inverse kinematics of an n–DOF (redundant) one are solved by a recursive and an iterative method, respectively. A numerical example is presented.

On the viscous flows of leak-out and spherical cap natation

2017 ◽  
Vol 836 ◽  
pp. 502-531 ◽  
Author(s):  
Rolf J. Ryham
Keyword(s):  
Closed Form ◽  
Flow Fields ◽  
The Body ◽  
Spherical Cap ◽  
Closed Form Solutions ◽  
Axis Of Symmetry ◽  
Freely Suspended ◽  
Limiting Case ◽  
Resistance Coefficients ◽  
Creeping Motion

This paper deals with the hydrodynamics of a viscous liquid passing through the hole in a deflating hollow sphere. I employ the method of complementary integrals and calculate in closed form the pressure and streamfunction for the axisymmetric, creeping motion coming from changes in radius. The resulting flow fields describe the motion of a deformable spherical cap in a viscous environment, where the deformations include changes in the size of the spherical cap, the size of the hole and translation of the body along the axis of symmetry. The calculations yield explicit expressions for the jumps in pressure and resistance coefficients for the combined deformations. The equation for the translation force shows that a freely suspended spherical cap is able to propel as an active swimmer. The expression for pressure contains the classic Sampson flow rate equation as a limiting case, but simulations show that the pressure must also account for the velocity of hole widening to correctly predict outflow rates in physiology. Movies based on the closed-form solutions visualize the flow fields and pressures as part of physical processes.

A New Algorithm for a Spatial Serial Robot

2010 ◽  
Vol 29-32 ◽  
pp. 952-955
Author(s):  
Xi Guang Huang ◽  
Guang Pin He ◽  
Duan Ling Li
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Greatest Common Divisor ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Serial Robot ◽  
Univariate Polynomial

In this paper a new algorithm to compute all the closed-form inverse kinematics solutions of a spatial serial robot. Based on the method, A 16th degree univariate polynomial of the spatial serial robot is obtained without factoring out or deriving the greatest common divisor. We also obtain all the closed-form solutions for the inverse kinematics of the robot. Finally a numerical example is given to demonstrate the algorithm process.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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