  We present an analytical solution for the inverse kinematics (IK) of a
robotic arm with one prismatic joint and four revolute joints. This 5-DoF
design is a result of minimizing weight while preserving functionality of the
device in a wearable usage context. Generally, the IK problem for a 5-DoF robot
does not guarantee solutions due to the system being over-constrained. We
obtain an analytical solution by applying geometric projections and limiting
the ranges of motion for each DoF. We validate this solution by reconstructing
randomly sampled end-effector poses, and find position errors below 2 cm and
orientation errors below 4 degrees.
