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.
Keywordsendless-Cable friction drive the Euler-Eytelwein’s formula statics
Unable to display preview. Download preview PDF.
This work was supported by JSPS KAKENHI Grant Number 18K04068.
- 4.Fortin-Côté, A., Faure, C., Bouyer, L., McFadyen, B.J., Mercier, C., Bonenfant, M., Laurendeau, D., Cardou, P., Gosselin, C.: On the Design of a Novel Cable-Driven Parallel Robot Capable of Large Rotation About One Axis. in Cable-Driven Parallel Robots, Mechanisms and Machine Science 53, pp. 390-401, Springer (2017). https://doi.org/10.1007/978-3-319-61431-133.
- 7.Makino, T., Harada, T.: Cable Collision Avoidance of a Pulley Embedded Cable-Driven Parallel Robot by Kinematic Redundancy. 4th International Conference on Control, Mechatronics and Automation, pp. 117-120, Barcelona (2016). https://doi.org/10.1145/3029610.3029620.
- 8.Meriam, J.J, Kraige, L.G.: Engineering Mechanics, Statics (Seventh Edition). pp. 377-378, John Wiley & Sons (2006). ISBN:978-0-470-61473-0.Google Scholar
- 10.Zitzewitz, J.V., Fehlberg, L., Bruckmann, T., Vallery, H.: Use of Passively Guided Deflection Units and Energy-Storing Elements to Increase the Application Range of Wire Robots. Cable-Driven Parallel Robots, Mechanisms and Machine Science 12, pp. 167-184, Springer (2013). https://doi.org/10.1007/978-3-642-31988-4_11.Google Scholar