Non-slipping Conditions of Endless-Cable Driven Parallel Robot by New Interpretations of the Euler-Eytelwein’s Formula

Non-slipping conditions of endless-cable driven parallel robot (E-CDPR) which enables unlimited rotation of the hand are discussed in this paper. Instead of fixing the end of the cable to the pulley and the winch, endless-cable (loop-cable) is turned around the endless-pulley and the endless-winch. Because friction forces between the cable and the drum transfer the cable tension, slipping of the cable which is dominated by the well-known Euler-Eytelwein’s formula is taking into consideration of the statics of the E-CDPR. In this paper, a new interpretation of the Euler-Eytelwein’s formula is proposed by using a graph that the non-slipping condition is expressed as an area in the cable tensions. Equations of the statics of the endless-pulley and the endless-winch are superimposed on the graph, then the non-slipping conditions of the E-CDPR are derived.