# Introduction to dynamics

• Alain Liégeois
Part of the Robot Technology book series (NSRDS, volume 7)

## Abstract

In this chapter the basic principles of dynamics involved in robotics are discussed. These underlying principles of the analysis and synthesis of articulated mechanical systems are discussed in the context of dynamic modelling by digital computer. Dynamics establishes relationships between forces and movement. Statics refers to the specific case where there is no movement relative to a fixed (or Galilean) frame of reference. For present purposes a force will be considered as a vector $$\underline{{{F}_{i}}}$$ linked to a three-dimensional space with the point of application Ai as its origin. The external forces (eg gravity, interactions with other bodies) represent the interaction of the body with its environment. Internal forces result from the interaction between various parts of the body, and can be ignored in the case of a body that is not flexible (ie rigid body). At a point P, the resultant of the external forces is defined (see Figure 3.1) as:
$$\underline{{{F}_{P}}}=\sum\limits_{i}{\underline{{{F}_{i}}}}$$
(3-1)
with the resulting moment:
$$\underline{{{M}_{P}}}=\sum\limits_{i}{\underline{P{{A}_{i}}}\wedge \underline{{{F}_{i}}}}$$
(3-2)
For an isolated rigid body, it is preferable to let P be the centre of inertia G of the body.

## Keywords

Rigid Body Lagrange Equation Industrial Robot Mechanical Chain Rigid Mode