scholarly journals Coupler-Point-Curve Synthesis Using Homotopy Methods

1990 ◽  
Vol 112 (3) ◽  
pp. 384-389 ◽  
Author(s):  
Lung-Wen Tsai ◽  
Jeong-Jang Lu
Keyword(s):  
Numerical Method ◽  
Continuation Method ◽  
Homotopy Method ◽  
Synthesis Problem ◽  
Singular Solutions ◽  
Homotopy Methods ◽  
Point Curve ◽  
Non Linear

A numerical method called “Homotopy Method” (or Continuation Method) is applied to the problem of four-bar coupler-curve synthesis. We have shown that: for five precision points, the “General Homotopy Method” can be applied to find the link lengths of number of four-bar linkages, and for nine precision points, a heuristic “Cheater’s Homotopy” can be applied to find some four-bar linkages. The nine-coupler-points synthesis problem is highly non-linear and highly singular. We have found that Newton-Raphson’s method and Powell’s method tend to converge to the singular solutions or do not converge at all, while the Cheater’s Homotopy always finds some non-singular solutions although sometimes the solutions may be complex.

scholarly journals Coupler-Point-Curve Synthesis Using Homotopy Methods

1989 ◽  
Author(s):  
L.-W. Tsai ◽  
J.-J. Lu
Keyword(s):  
Numerical Method ◽  
Continuation Method ◽  
Homotopy Method ◽  
Synthesis Problem ◽  
Singular Solutions ◽  
Homotopy Methods ◽  
Point Curve ◽  
Non Linear

Abstract A numerical method called “Homotopy Method” (or Continuation Method) is applied to the problem of four-bar coupler-point-curve synthesis. We have shown that: for five precision points, the “General Homotopy method” can be applied to find the link lengths of a number of four-bar linkages, and for nine precision points, a heuristic “Cheater’s Homotopy” can be applied to find some four-bar linkages. The nine-coupler-points synthesis problem is highly non-linear and highly singular. We have found that Newton-Raphson’s method and Powell’s method tend to converge to the singular solutions or do not converge at all, while the Cheater’s Homotopy always finds some non-singular solutions although sometimes the solutions may be complex.

Conduction of heat in a solid with periodic boundary conditions, with an application to the surface temperature of the moon

1953 ◽  
Vol 49 (2) ◽  
pp. 355-359 ◽  
Author(s):  
J. C. Jaeger
Keyword(s):  
Boundary Condition ◽  
Thermal Properties ◽  
Circular Cylinder ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Numerical Method ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
The Moon ◽  
Non Linear

The object of this note is to indicate a numerical method for finding periodic solutions of a number of important problems in conduction of heat in which the boundary conditions are periodic in the time and may be linear or non-linear. One example is that of a circular cylinder which is heated by friction along the generators through a rotating arc of its circumference, the remainder of the surface being kept at constant temperature; here the boundary conditions are linear but mixed. Another example, which will be discussed in detail below, is that of the variation of the surface temperature of the moon during a lunation; in this case the boundary condition is non-linear. In all cases the thermal properties of the solid will be assumed to be independent of temperature. Only the semi-infinite solid will be considered here, though the method applies equally well to other cases.

Sign in / Sign up

Export Citation Format

Share Document