A unified framework for tolerance analysis of planar and spatial mechanisms using screw theory

• Screw theory is applied to both planar and spatial mechanisms.
• Manufacturing errors are modeled as virtual screws.
• Actual profiles or surfaces deviate from nominal due to manufacturing errors.
• Following the intent of ISO, normal distance is used to quantify the deviation.
• Pattern and value of the deviations in the mechanisms are known a priori.

Kinematic accuracy of path traced by a chosen point of a given mechanism is affected by manufacturing errors that cause variation in link lengths and joint clearances. Tolerance analysis in mechanisms refers to a process of finding out deviation from nominal path of the given point in the mechanism due to the manufacturing errors. In this paper, a new application of screw theory is proposed to analyze the kinematic accuracy of the mechanisms with variations in link lengths and joint clearances. Potential of the proposed approach is demonstrated by its application to the tolerance analysis of four-bar planar mechanisms. Following the intent of the international standard, the deviation from nominal path is quantified in normal direction which is more meaningful from a practical perspective. Applicability of the proposed approach to a spatial mechanism is demonstrated using a serial manipulator with three-revolute joints and having one joint-error. The unified framework presented in this paper can be applied conveniently for closed as well as open loop serial manipulators. Designers can use the results of such analysis to specify the tolerances to achieve a desired degree of kinematic accuracy.