An earlier study introduced a formula for determining the holding force of a toroidal hydrostat gripper when gripping an object of constant radius, considering a linear stress/strain relationship. However, beyond the holding force, understanding the grasping disturbance force exerted on the object due to the rolling behavior during grip adjustment is crucial to ensure the objects are not damaged or displaced, and are successfully picked up. This study aims to extend the existing model by incorporating the disturbance force for objects with variable radii and using a non-linear stress/strain relationship for the membrane material.
A parametric model was developed to estimate these forces as a function of its geometric and material properties. The model was validated through experimental testing and refined using a tuning parameter obtained via optimization algorithms to address parameter uncertainties.
The model approximated the holding forces well, with a maximum deviation of 15\% at the maximum swallow distance. It overestimated the peak disturbance forces by a factor of 2.5. But when normalized, the force curves showed good resemblance.
Surprisingly, the obtained tuning parameter reached a high value of $1.45$. as the parameter uncertainties are thought to be less than 20%. This overestimation could be the result of an additional vacuum force, as evidenced by a clear difference in holding force and gripper behavior is observed in pulling tests for objects with smooth and rough surfaces.