Analysis of the displacement of lumped compliant parallel-guiding mechanism considering parasitic rotation and deflection on the guiding plate and rigid beams

•A new mathematical model discussed from four different situations is established.•In situation D, both the parasitic rotation and deflection are taken into account.•The displacements are analyzed at different distances between two supporting arms.

Lumped compliant parallel-guiding mechanism (CPGM) is a particular type of compliant mechanisms. This paper establishes a new mathematical model of the lumped-CPGM based on the elastic beam (EB) theory with an increasing precision discussed from four different situations. In situation D, both the parasitic rotation and deflection of the guiding plate and rigid beams are taken into account, which might be tiny but do exist in reality. As for a comparison, a pseudo-rigid-body (PRB) model is also established. Then the guiding displacement, parasitic displacement and parasitic angle in the four situations are analyzed at different distances between two supporting arms, which have not been involved by any former researchers. Furthermore, the relations between the displacements and some other structural parameters are analyzed respectively comparing with the finite element method. The results indicate that the EB model in situation D is very effective with a much higher precision than other models, although the computation is more complicated. Our work could be a reference and supplement to the design and manufacture of the current lumped-CPGM.