This text provides a first-level understanding of the structure, mobility, and analysis of serial manipulators. A serial manipulator is an unclosed or open movable polygon consisting of a series of links and joints. One end is fixed to ground, and attached to the open end is a hand or end effector that can move freely in space.

The structure of a serial manipulator is established by labeling the skeletal form (the sequence of joints and links) with appropriate twist angles and perpendicular distances that define the relative positions of sequences of pairs of skew lines. In this way the geometry of the manipulator is defined, and subsequently it is possible to apply various coordinate transformations for points located on the links. Such transformations readily provide a so-called forward analysis, that is, they can be used to provide the position of some point on the end effector together with the orientation of the end effector measured relative to a coordinate system fixed to ground for a specified set of joint variables.

A more difficult problem is the solution of the so-called reverse or inverse analysis. Here, the position of a point on the end effector together with the end effector's orientation is specified. It is required to determine a corresponding set of six joint variables that will position and orient the end effector as desired. There are multiple solution sets of the six joint variables, in contrast to the forward analysis, where only one solution exists.