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The manipulability index suggested by Yoshikava is an important tool for the design of mechanisms and their control. It represents a quantitative measure of the functionality and the ability for realizing some tasks or groups of tasks. This index is some kind of performance measure and should be taken into consideration in the design phase of a mechanism and also in the design of control algorithms.In this paper two important properties of the manipulability index are investigated. The first part of the present work demonstrates that manipulability of a mechanism is independent of task space coordinates. In the second part, a proof of the independency of the manipulability index on the first DOF is given.This invariance is important for simplification of the mechanism's Jacobian matrix and gives excellent insight into the dependences of configuration space coordinates on this index. Moreover, it proves that the manipulability index is determined only by relative positions of the mechanism itself and by the mechanism's geometry.Finally, the properties of the manipulability index are illustrated by some examples for fundamental open kinematical chain structures.

Demonstrates the modelling of the kinetic process when the sewing needle enters the fabric. To get an adequate mechanical model of the given problem, the function ‐ the mathematical model ‐ of the penetration force with respect to the fabric, the needle and the mechanism in the sewing machine must be developed. The fabric was modelled as a combination of warp and weft threads. Each thread from the fabric is modelled as an ideal elastic Hook’s material. Outlines the restrictions which needed to be made to get the mathematical model of the problem.

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