Vertical Vibratory Transport of Grasped Parts Using Impacts

TL;DR

The study addresses lifting grasped parts upward against gravity via 1D vertical vibrations, revealing gravity makes upward transport more demanding than horizontal due to friction cone skewing. A Coulomb-friction-based dynamical model stipulates conditions $F_n > m_P g / \mu_s$ and $a_{max} > \mu_s F_n / m_P + g$ (with $a_{max} > 2g$) and shows optimal transport reduces to a horizontal-like problem under transformed friction, yielding an optimal three-phase stick-slip waveform. Impact-driven accelerations are employed to realize the required high $a_{max}$, and the model is validated experimentally with a vibrating-surface device and motion tracking, including a proof-of-concept vibrating-gripper that handles diverse parts. The results establish design guidelines for large normal forces and rapid accelerations to achieve upward vibratory transport, with potential applications in in-hand planar manipulation and multi-surface, closed-loop grasping systems.

Abstract

In this paper, we use impact-induced acceleration in conjunction with periodic stick-slip to successfully and quickly transport parts vertically against gravity. We show analytically that vertical vibratory transport is more difficult than its horizontal counterpart, and provide guidelines for achieving optimal vertical vibratory transport of a part. Namely, such a system must be capable of quickly realizing high accelerations, as well as supply normal forces at least several times that required for static equilibrium. We also show that for a given maximum acceleration, there is an optimal normal force for transport. To test our analytical guidelines, we built a vibrating surface using flexures and a voice coil actuator that can accelerate a magnetic ram into various materials to generate impacts. The surface was used to transport a part against gravity. Experimentally obtained motion tracking data confirmed the theoretical model. A series of grasping tests with a vibrating-surface equipped parallel jaw gripper confirmed the design guidelines.

Figures (8)

• Figure 1: Vibrating surfaces lift a part against gravity.
• Figure 2: Kinematics and dynamics. The part, $P$, and the surface, $S$ are constrained to move purely along the $\Vec{e_z}$ direction. The rollers on the left side of $P$ indicate sliding on a frictionless surface.
• Figure 3: Nondimensional accelerations, velocities, and positions of the surface (blue) and part (red) given $f_n = 5$ and $a_{max} = 10g$. Despite the surface achieving $10g$ of acceleration, which is used to slip below and catch up to the part, the part's velocity does go negative unlike in previous work umbanhowar2008optimal.
• Figure 4: Average normalized velocity versus the normal force per part weight ($f_n$), when $\mu_s = 0.7$ and $\mu_k = 0.6$. Average normalized velocity curves for a given $a_{max}$ are denoted by the dotted lines and several callouts; lighter colors indicate curves with higher maximum accelerations. The red line indicates the value of $f_n$ that maximizes $\frac{v_{ave}}{gT}$ for a given $a_{max}$. Note that this optimal $f_n$ can be an order of magnitude or greater than the force required to statically hold the part. The normal force at which a given $a_{max}$ curve intersects the dotted line given by $\frac{v_{ave}}{gT} = 0$ is $f_{n,max}$.
• Figure 5: Schematic of experimental setup is shown in (A), with the constructed setup shown in (B) and a section view of the impact motor in (C). (A, B) The vibrating surface $S$ is shown on the right and the constant force springed plate is shown on the left. Movement of the ram inside the motor causes the surface to move. Flexure stiffness and actuator-platform assembly mass were minimized to avoid filtering movement of the ram. A screw and linear spring are used to adjust the normal force applied to $P$. Note that springed plate assembly in (B) is viewed from above for clarity, as the shoulder bolts and spring lie in the same plane. (C) The magnetic suspension holds the ram at an equilibrium position. The coil can move the ram towards the suspension, which repels the ram, or away from the suspension possibly generating a collision with the impact wall.