3.3 Transforming Kinematic Chains of Bodies

The transformations become more complicated for a chain of attached rigid bodies. For convenience, each rigid body is referred to as a link. Let ${\cal A}_1$, ${\cal A}_2$, ..., ${\cal A}_m$ denote a set of $m$ links. For each $i$ such that $1 \leq i < m$, link ${\cal A}_i$ is ``attached'' to link ${\cal A}_{i+1}$ in a way that allows ${\cal A}_{i+1}$ some constrained motion with respect to ${\cal A}_i$. The motion constraint must be explicitly given, and will be discussed shortly. As an example, imagine a trailer that is attached to the back of a car by a hitch that allows the trailer to rotate with respect to the car. In general, a set of attached bodies will be referred to as a linkage. This section considers bodies that are attached in a single chain. This leads to a particular linkage called a kinematic chain.