Modeling assembly quality requirements using Jacobian or screw transforms: a comparison

This paper presents a comparison between two currently available tools used to mathematically model the contribution of toleranced dimensions on critical quality requirements of an assembly, namely the screw based approach and the Jacobian based approach. It is shown that both models are actually equivalent, in the sense that the Jacobian based model can be broken down into a screw based model using first order approximations, and that conversely the screw approach can be made equivalent to a Jacobian based approach by expressing deviations remotely instead of locally.