Simplified model to study the kinematics of manipulators with parallelogram linkages

Purpose Parallelogram linkages are used to increase the stiffness of manipulators and allow precise control of end-effectors. They help maintain the orientation of connected links when the manipulator changes its position. They are implemented in many palletizing robots connected with binary, ternary and quaternary links through both active and passive joints. This limits the motion of some joints and hence results in relative and negative joint angles when assigning coordinate axes. This study aims to provide a simplified accurate model for manipulators built with parllelogram linkages to ease the kinematics calculations. Design/methodology/approach This study introduces a simplified model, replacing each parallelogram linkage with a single (binary) link with an active and a passive joint at the ends. This replacement facilitates countering motion while preserving subsequent link orientations. Validation of kinematics is performed on palletizing manipulators from five different OEMs. The validation of Dobot Magician and ABB IRB1410 was carried out in real time and in their control software. Other robots from ABB, Yaskawa, Kuka and Fanuc were validated using control environments and simulators. Findings The proposed model enables the straightforward derivation of forward kinematics and transforms hybrid robots into equivalent serial-link robots. The model demonstrates high accuracy streamlining the derivation of kinematics. Originality/value The proposed model facilitates the use of classical methods like the Denavit–Hartenberg procedure with ease. It not only simplifies kinematics derivation but it also helps in robot control and motion planning within the workspace. The approach can also be implemented to simplify the parallelogram linkages of robots with higher degrees of freedom such as the IRB1410.