Pin Design for Part Feeding

Mike Tao Zhang and Ken Goldberg
<August, 1998 ~ August, 1999 > 
ALPHA Lab, University of California, Berkeley. 
 
 


Abstract:

We consider a sensorless approach to feeding parts on a conveyor belt using pins (rigid barriers) to topple parts into desired orientations. Given the n-sided 2D convex projection of an extruded polygonal part, its center of mass (COM), and coefficients of friction, we develop an O(n2) algorithm to compute the toppling graph, a new data structure that represents the mechanics of toppling including rolling and jamming. The toppling graph can be used to identify critical pin heights that permit toppling. We compare pin heights predicted by the graph with physical experiments, and give a complete O(n3n) algorithm for designing pin sequences.
 
 

Introduction:

There is a growing demand for automated manipulation analysis, especially efficient algo-rithms, for modern manufacturing. Efficient algorithms can be incorporated to commercial CAD/CAM software packages to facilitate rapid setup and changeover of assembly lines. 

Lynch1 analyzes how a part can be toppled by programmable pins to a new orientation as it moves on a conveyor belt.  In this paper we extend his analysis with a geometric algorithm for designing fixed pin sequences for part feeding.

Given the n-sided 2D convex projection of an extruded polygonal part, its center of mass, and coefficients of friction, we want to find a sequence of the pins (if exists) such that the part emerges in a unique final orientation after moving through. The first step is to find the critical pin heights at each of the part’s stable orientation where the pin can topple the part from one stable orientation to the next; the second step is to solve a planing problem to design an ar-rangement of the pins.

Our analysis involves the graphical construction of a set of functions that represent the mechanics of toppling. The toppling graph is a new data structure that combines these functions to help us to identify the critical pin heights. 
 
 



Publications:

  • T. Zhang, K. Goldberg, Gordon Smith, Robert-Paul Berretty, and Mark Overmars. "Pin design for part feeding," Robotica, Cambridge University Press (accepted). [PDF]
  • T. Zhang, G. Smith, R. Berretty, M. Overmars, and K. Goldberg. "The toppling graph: designing pin sequences for part feeding," in IEEE International Conference on Robotics and Automation, San Francisco, 2000. 

Acknowledge:

    This work was supported in part by NATO Collaborative Research Grant CRG 951224, the National Science Foundation under CDA-9726389 and Presidential Faculty Fellow Award IRI-9553197.