Analytical Inverse Kinematics for a 5-DoF Robotic Arm with a Prismatic Joint

TL;DR

This paper introduces an analytical inverse kinematics solution for a lightweight 5-DoF robotic arm with one prismatic joint, suitable for wearable applications, achieving accurate end-effector positioning and orientation.

Contribution

It provides the first analytical IK solution for a 5-DoF robot with a prismatic joint, addressing over-constrained challenges through geometric methods and motion range limitations.

Findings

Position errors below 2 cm

Orientation errors below 4 degrees

Validated with randomly sampled end-effector poses

Abstract

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.