On the forward displacement problem of three-branch parallel manipulators

Abstract

Solutions for the forward displacement problem (FDP) are presented for three-branch parallel manipulators. Considered are all three-branch manipulators where each branch is comprised of a serial arrangement of three main-arm joints supporting a common payload platform through a passive spherical joint group at the branch end. All feasible combinations of revolute and prismatic joints and all feasible combinations of sensing of the main-arm joints are considered. Intersection of loci defining the feasible locations of the branch ends considering individual branches and branch combinations is utilized to identify FDP solutions. It is demonstrated that analytical FDP solutions can be found for all cases of redundant sensing (seven, eight or nine sensors) of the main-arm joint displacements. Furthermore, it is shown that with asymmetric distribution of non-redundant sensing (six sensors) an analytical solution can also be found. The maximum number of assembly modes and necessary conditions required for the maximum numbers are identified for all cases. Appropriate sensing redundancy is concluded to be an important consideration in the design of parallel manipulators since it facilitates an ability to have direct analytical FDP solutions; a reduction of the potential assembly modes; and the potential of sensor-failure-safe implementations.