Capstan equation

The change in rope tension is described by the well-known Euler or capstan equation. The two variations for lowering and raising a load are... 

The Capstan equation can be rewritten to give the fiiction coefficient of fibers on other materials ... 

Note that the actuator s rotors also contribute to the apparent mass of the robot. To estimate their contribution, the same reasoning can be applied, with all equations expressed, however, at the motor level. It can be proven that the apparent inertia of the actuators increases as a fimction of R. As a consequence, the inertia of systems using large reducers, for example, harmonic drives, is relatively important (often larger than the links apparent inertia) and requires force-sensing and force-control closed loops to reduce it. On the contrary, the inertia of actuation units using low-reduction-ratio cable capstan reducers is usually very limited (much smaller than the link s inertia). 

The friction of yam to yam is measured by moving yam at known speed in contact with itselfThe input and output tensions are measured and the coefficients of friction are calculated. Two methods of determination are used. In the Capstan method, the coefficient of friction is calculated from equation [3.3]. In the twisted strand method, the equation is modified to account for twist characteristics. 

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