Part orientation with one or two stable equilibria using programmable force fields

Abstract

Programmable force elds are an abstraction to represent a new class of devices for distributed, nonprehensile manipulation for applications in parts feeding, sorting, positioning, and assembly. Unlike r o b o t grippers, conveyor belts, or vibratory bowl feeders, these devices generate force vector elds in which the parts move u n til they may reach a stable equilibrium pose.Recent research in the theory of programmable force elds has yielded open-loop strategies to uniquely position, orient, and sort parts. These strategies typically consist of several elds that have to be employed in sequence to achieve a desired nal pose. The length of the sequence depends on the complexity of the part.In this paper, we show that unique part poses can be achieved with just one eld. First, we exhibit a single eld that positions and orients any part (with the exception of certain symmetric parts) into two stable equilibrium poses. Then we show that for any part there exists a eld in which the part reaches a unique stable equilibrium pose (again with the exception of symmetric parts). Besides giving an optimal upper bound for unique parts positioning and orientation, our work gives further evidence that programmable force elds are a powerful tool for parts manipulation.Our second result also leads to the design of \universal parts feeders", proving an earlier conjecture about their existence. We argue that universal parts feeders are relatively easy to build, and we report on extensive s i m ulation results which indicate that these devices may w ork very well in practice. We believe that the results in this paper could be the basis for a new generation of e cient, open-loop, parallel parts feeders.

A Single Universal Force Field Can Uniquely Orient Non-Symmetric Parts

“…The proof of this proposition can be found in [7]. Proposition 3 states that a stable equilibrium configuration corresponds to a value of i where the equilibrium curve crosses the y-axis from …”

“…An extensive survey of previous and related work in the area of programmable force fields is offered in [7]. In this paper we only give a brief summary.…”

“…and we define the following potential field over the configuration space b of the part: The proof of this proposition can be found in [7].…”

Part assembly using static and dynamic force fields

“…One interesting class of force fields are potential fields in which the work integral is zero along any circular path. Such fields are the squeeze field [3,4,11], the elliptical field [3,7,11], and the radial plus gravity field [3,8]. These potential fields can translate and rotate a part to equilibrium configurations.…”

“…They are the squeeze, elliptical, and radial plus gravity fields. A polygonal part can be uniquely oriented up to symmetries with a sequence of squeeze fields [3,4]. However, we have to select different sequences of squeeze fields for different parts.…”