Analysis of mutual interaction between joints of robots with branched kinematic chains

In this work dynamic couplings were presented, which occur in the kinematic chains of branched positioning systems, e.g.: medical robots da Vinci. Replacing torque generated by driveline by gravity force allows authors to treat branched manipulators as a branched pendulum, in which interactions between the different branches occur. Basing on the methodology of mathematical modeling of robots´ manipulators, in this article is presented mathematical models of chosen branched manipulators. For all researched branched kinematic chains the dynamics matrices were prepared, and their internal structure expressed. Resultant dynamics matrices have block structure, in which some block was isolated and it denotes the self-inertial dynamics matrices of bough and branches, as well the bough-branch mutual interaction inertial matrices. Formulated mathematical models for positioning systems were simulated in MATLAB / Simulink, presenting them as a pendulum. Among examined chains there was selected kinematic chain, in which the interaction between the branches were the greatest, and then using the 3D printer there was made its model at the macro level. Using low-cost MEMS sensors attached on the axis of rotation of the individual branches displacements were measured indirectly. The results were compared with the results of the simulation. On the basis of results of simulations and measurements there were presented, which of manipulators´ configurations are predisposed to mutual couplings in branched-chain positioning systems. For calculating angular positions Kalman filter for sensor fusion was used.