Three-Dimensional Mathematical Model of Bio-Mechanical System: Human- Mechanized Hand Tool in Accordance to ISO 10068 Standard on the Example of Impact Drill

Abstract

This paper presents the development of a mathematical model of a bio-mechanical system: human ‒ power tool, on the example of an impact drill. The physical model of the operator's upper limb with 5 degrees of freedom, in accordance with ISO 10068 standard was used. The paper presents the results of theoretical analysis regarding elementary and net displacements for individual directions. Moreover mathematical relationships describing them were determined. The result of the synthesis of these relations and the adopted (in accordance with the standard) physical model of the upper limb is the general matrix form of differential equations of motion of the analysed bio-mechanical system, built using the Lagrange’s equations of the second kind.