Error modeling of the carpal wrist

Abstract

In recent years, increased emphasis has been placed on the development of parallel-architecture mechanisms for use as robotic manipulators. Parallel robots offer the benefits of higher load-carrying capacity, greater positioning accuracy and lower weight when compared to serial devices. However, robotic wrist development has traditionally focused on serial mechanisms having a large, spherical workspace and simpler kinematic solutions. The Carpal wrist is a unique parallel mechanism consisting of a fixed base and a movable output plane connected via three serial kinematic chains. The forward and inverse kinematic problems of the Carpal wrist are solved closed-form, making the device suitable for use as a new type of robotic wrist. The closed-form solutions are dependent upon the assumptions that the fixed and moving planes are symmetric about a mid-plane and that the three kinematic chains connecting the planes are identical. This thesis investigates the errors that result from those assumptions being violated due to manufacturing and assembly errors. In the non-ideal model, pose error is found by iteratively solving a system of equations describing the output plane position and orientation and comparing them with the ideal solution. The error model is a tool for predicting the effects of kinematic parameter errors on the positioning accuracy and reachable workspace of the Carpal wrist. In this work, a general error model is developed and validated for a range of parameter error values. Special-case results are presented for errors in the individual parameters.