Principal Contributions - Applications
The isotropic vector problem is proposed and solved. An algorithm is developed to construct orthonormal sets of isotropic vectors.
Using isotropic vectors, the stiffness synthesis by springs problem is fully solved.
Free-vector and line-vector decompositions are applied to the synthesis problem leading to minimum syntheses.
Design equations for RCC devices are determined.
Rotational symmetry devices are proposed as generalized RCCs. Design equations are found.
The theory of stiffness is applied to the spatial mass matrix. The eigen- and co-eigenscrew structure is fully determined.
The mass matrix results explains and generalizes the concept of percussion center.
Combining the stiffness and mass matrix results, the necessary and sufficient condition for special free-vibration modes are found.