Computer generation of normalizing transformation for systems of nonlinear ODE

1993 ◽  
Author(s):  
Victor F. Edneral
Keyword(s):  
Normalizing Transformation ◽  
Nonlinear Ode ◽  
Computer Generation

Robot Workspace of a Tool Plane: Part 2—Computer Generation and Selected Design Conditions for Dexterity

1987 ◽  
Vol 109 (1) ◽  
pp. 61-71 ◽  
Author(s):  
J. K. Davidson ◽  
P. Pingali
Keyword(s):  
Ruled Surface ◽  
End Effector ◽  
Plane Part ◽  
Computer Generation ◽  
Robot Workspace

In this paper the algorithm is completed for generation of envelope-surfaces for plane-workspaces of generally proportioned manipulators. Then the ruled surface Ψ is used for adapting the algorithm to 3-R manipulators for which the outermost two axes intersect (a2 = 0). The discriminant D is further developed, and it is used to classify 3-R manipulators, having a2 = 0, into seven Types. Manipulators, which are of Type 7, (i) can provide any orientation to a tool plane σ or (ii), with a fourth appropriately placed R joint and tool plane Σ, can also provide any attitude to the end effector. Design conditions are developed and presented which ensure that a manipulator will possess these properties of dexterity. The conditions are based on coupled motions at all three, or four, axes.

A FORMULA FOR NORMALIZING TRANSFORMATION OF SOME STATISTICS

2002 ◽  
Vol 31 (2) ◽  
pp. 163-179 ◽  
Author(s):  
Nobuhiro Taneichi ◽  
Yuri Sekiya ◽  
Akio Suzukawa ◽  
Hideyuki Imai
Keyword(s):  
Normalizing Transformation

A Computational Tool for the Reduction of Nonlinear ODE Systems Possessing Multiple Scales

2005 ◽  
Vol 4 (3) ◽  
pp. 732-759 ◽  
Author(s):  
Robert Clewley ◽  
Horacio G. Rotstein ◽  
Nancy Kopell
Keyword(s):  
Multiple Scales ◽  
Computational Tool ◽  
Nonlinear Ode ◽  
Ode Systems
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