Closed-Form Non-Singular Constant-Curvature Continuum Manipulator Kinematics

2020 ◽  
Author(s):  
Thomas F. Allen ◽  
Levi Rupert ◽  
Timothy R. Duggan ◽  
Gabriel Hein ◽  
Kevin Albert
Keyword(s):  
Closed Form ◽  
Constant Curvature ◽  
Continuum Manipulator

On the Contact Problem of Thin Circular Rings

1965 ◽  
Vol 32 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Chien-Heng Wu ◽  
Robert Plunkett
Keyword(s):  
Contact Problem ◽  
Closed Form ◽  
Constant Curvature ◽  
Complete Solution ◽  
Elliptic Functions ◽  
Numerical Results ◽  
Elastic Contact ◽  
Flat Plates ◽  
Circular Rings

It is well known that the solution of an elastica subjected to end loads can be obtained in terms of elliptic functions. In the present paper, the combined problem of elastic contact between uniform circular rings or cylinders is reduced to a set of end-loaded elasticas. The approach is demonstrated by finding the complete solution in closed form for two unequal rings pressed between rigid anvils of constant curvature. Numerical results are obtained for the set of problems of two rings with equal stiffness but unequal radii compressed between two rigid flat plates.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

Sign in / Sign up

Export Citation Format

Share Document