I.2 - Fundamentals

Abstract

The number of degrees of freedom (DOF) of a system is equal to the number of independent parameters (measurements) that are needed to uniquely define its position in space at any instant of time. The number of DOF is defined with respect to a reference frame. Six parameters are needed to define the position of a free rigid body in a three-dimensional (3-D) space. One possible set of parameters that could be used are three lengths, (x, y, z), plus three angles (θx, θy, θz). Any free rigid body in 3-D space has six degrees of freedom. A rigid body free to move in a reference frame will, in general case, have complex motion, which is simultaneously a combination of rotation and translation. Linkages are basic elements of all mechanisms. Linkages are made up of links and joints. A link, sometimes known as an element or a member, is an (assumed) rigid body, which possesses nodes. Nodes are defined as points at which links can be attached. A link connected to its neighboring elements by “s” nodes is an element of degree “s.”