Formulating Assur kinematic chains as projective extensions of Baranov trusses

The real roots of the characteristic polynomial of a planar linkage determine its assembly modes. In this work it is shown how the characteristic polynomial of a Baranov truss derived using a distance-base formulation contains all the necessary and sufficient information for solving the position analysis of the Assur kinematic chains resulting from replacing some of its revolute joints by slider joints. This is a relevant result because it avoids the case-by-case treatment that requires new sets of variable eliminations to obtain the characteristic polynomial of each Assur kinematic chain.

► A theory for the position analysis of Assur kinematic chains in terms of distances ► The analysis of Assur kinematic chains is reduced to the analysis of Baranov trusses. ► The case-by-case study of Assur kinematic chains by using loop equations is avoided. ► The approach is exemplified by solving a family of 7-link Assur kinematic chains.