A Note on the Determination of the Thermal Stresses in Multi-Metal Beams Subjected to Temperature Variations

1991 ◽  
Vol 113 (4) ◽  
pp. 425-427 ◽  
Author(s):  
A. O. Cifuentes
Keyword(s):  
Linear System ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Technical Note ◽  
Form Solution ◽  
System Of Equations ◽  
Temperature Variations ◽  
Temperature Changes ◽  
Linear System Of Equations

This technical note shows that the determination of the stresses induced in multi-metal beams by temperature changes reduces to solving a linear system of equations. This system of equations has a very particular structure that allows one to obtain a closed form solution easily.

Kinematic Synthesis of Spatial R-R Dyads for Path Following With Applications to Coupled Serial Chain Mechanisms

1999 ◽  
Vol 123 (3) ◽  
pp. 359-366 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Linear System ◽  
Optimal Path ◽  
Closed Form Solution ◽  
Path Following ◽  
Form Solution ◽  
Dimensional Synthesis ◽  
Linear System Of Equations ◽  
Serial Chain ◽  
Position Problem ◽  
Additional Constraints

The dimensional synthesis of a spatial two revolute jointed dyad for path following tasks with applications to coupled serial chain mechanisms is presented. The precision point synthesis equations obtained using the rotation matrix approach form a rank-deficient linear system in the link-vector components. The nullspace of this rank-deficient linear system is derived analytically and interpreted geometrically. The nullspace vectors lead to the specification of additional constraints via the so-called auxiliary equations and to the solution of the linear system of equations. The geometry also allows the derivation of a closed form solution for the three design position problem. Finally, optimal path following by coupled R-R dyads is achieved by optimization over the free choice variables.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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