A systems model and simulation of the vibratory bowl feeder
TL;DR: In this paper, a mathematical model of a bowl feeder was developed by using state-space methods to evaluate bowl-feeder parameters, and a computer simulation can predict the velocity of the parts in the bowl and subsequently the part feed rate.
About: This article is published in Journal of Manufacturing Systems.The article was published on 1997-01-01. It has received 70 citations till now.
Citations
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TL;DR: In this article, a compliant platform based on the von Mises compliance matrix is proposed for a bowl feeder, which is decomposed into a central compliance matrix and an adjoint transformation leading to the decomposition of the legs' parameter effect from the platform assembly influence.
Abstract: The platform based vibratory bowl feeders are essential elements in automatic assembly. Taking the bowl feeder as a typical three-legged rigidly connected compliant platform device, this paper applies von Mises' compliance matrix to each of the leaf-spring legs, establishes screw systems of the legs and develops the Jacobian of the platform using the adjoint transformation. Based on the force equilibrium between the supporting and external wrenches and the twist deflection, a platform compliance matrix is proposed as a congruence transformation of the legs' compliance matrices. The matrix is then decomposed into a central compliance matrix and an adjoint transformation, leading to the decomposition of the legs' parameter effect from the platform assembly influence. The analysis presents the necessary and sufficient condition for the existence of the twist deflection that is equivalent to the characteristics equation of the compliant platform. Further based on the eigencompliances and eigentwist decomposition, the legs' parameter effect and the platform assembly parameter influence are identified. This reveals the compliance characteristics of this type of devices and the parameters' effect on the compliance and presents a suitable parameter range for design of the compliant platform device.
91 citations
01 Oct 1999
TL;DR: This is the first paper to systematically compare alternative estimators for solving the pose statistics of coins and dice as they are dropped on a flat surface and to correlate their performance with statistically significant experiments on industrial parts.
Abstract: Many of the most fundamental examples in probability involve the pose statistics of coins and dice as they are dropped on a flat surface. For these parts, the probability assigned to each stable face is justified based on part symmetry, although most gamblers are familiar with the possibility of loaded dice. In industrial part feeding, parts also arrive in random orientations. We consider the following problem: given part geometry and parameters such as center of mass, estimate the probability of encountering each stable pose of the part. We describe three estimators for solving this problem for polyhedral parts with known center of mass. The first estimator uses a quasistatic motion model that is computed in time O(n log n) for a part with n vertices. The second estimator has the same time complexity but takes into account a measure of dynamic stability based on perturbation. The third estimator uses repeated Monte Carlo experiments with a mechanics simulation package. To evaluate these estimators, we used a robot and computer vision system to record the pose statistics based on 3595 physical drop experiments with four different parts. We compare this data to the results from each estimator. We believe this is the first paper to systematically compare alternative estimators and to correlate their performance with statistically significant experiments on industrial parts.
57 citations
Cites background from "A systems model and simulation of t..."
...ulation [3], [17], [24], heuristics [20], and genetic algorithms...
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TL;DR: A class of vibratory bowl filters that can be described by removing polygonal sections from the track are considered, referred to as traps, which will filter out all but one of the different stable orientations of a given part.
Abstract: The vibratory bowl feeder is the oldest and still most common approach to the automated feeding (orienting) of industrial parts. In this paper, the authors consider a class of vibratory bowl filters that can be described by removing polygonal sections from the track; this class of filters is referred to as traps. For an n-sided polygonal part and an m-sided polygonal trap, an O(n2m log n) algorithm is given to decide whether the part in a specific orientation will safely move across the trap or will fall through the trap and thus be filtered out. For an n-sided convex polygonal part and m-sided convex polygonal trap, this bound is improved to O((n+m) log n). Furthermore, the authors show how to design various trap shapes, ranging from simple traps to general polygons, which will filter out all but one of the different stable orientations of a given part. Although the runtimes of the design algorithms are exponential in the number of trap parameters, many industrial part feeders use few-parameter traps (ba...
50 citations
Cites methods from "A systems model and simulation of t..."
...Specific to these vibratory bowls, researchers have used simulation (Berkowitz and Canny 1996; Jakiela and Krishnasamy 1993; Maul and Thomas 1997 ), heuristics (Lim et al. 1994), and genetic algorithms (Christiansen, Edwards, and Coello 1996) to design traps....
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10 May 1999
TL;DR: A class of vibratory bowl filters that can be described by removing polygonal sections from the track is considered; this class of filters are referred to as traps and two rectilinear subclasses, balconies and gaps are considered.
Abstract: The vibratory bowl feeder is the oldest and still most common approach to the automated feeding (orienting) of industrial parts. We consider a class of vibratory bowl filters that can be described by removing polygonal sections from the track; we refer to this class of filters as traps. For an n-sided convex polygonal part and m-sided convex polygonal trap, we give an O((n+m)log(n+m)) algorithm to decide if the part will be rejected by the trap, and an O((nm(n+m))/sup 1+/spl epsiv//) algorithm which deals with non-convex parts and traps. We then consider the problem of designing traps for a given part, and consider two rectilinear subclasses, balconies and gaps. We give linear and O(n/sup 2/) algorithms for designing feeders and have tested the results with physical experiments using a commercial inline vibratory feeder.
39 citations
Cites methods from "A systems model and simulation of t..."
...Specific to vibratory bowls, researchers have used simulation [14, 4, 19], heuristics [16], and genetic algorithms [10] to design traps....
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TL;DR: In this paper, the authors examined the use of a saw-tooth surface with a simple planar and symmetric vibration for a unidirectional microparts feeding.
Abstract: This paper examines the novel use of a saw-tooth surface with a simple planar and symmetric vibration for a unidirectional microparts feeding. In the microparts feeding, to drive the microparts in one direction, the driving force applied to each micropart must vary according to the direction of motion of the micropart. In the case of a saw-tooth surface, either the point or the slope of the saw-tooth can make contact with a micropart. The microparts move in one direction by the driving force according to the contact between the microparts and the saw-tooth surface. The feeding experiments show that the unidirectional feeding is achieved by the proposed method. The driving force at each contact and the dynamics of the microparts with adhesion force were formulated for the feeding simulations. Regarding the elevation angle at which the velocity was maximum, there was a good agreement between the simulation with adhesion force and the experimental values
31 citations
Cites background from "A systems model and simulation of t..."
...The most popular are the vibratory bowl-type feeders [2]–[4], whereby revolving vibrators are used to move parts along a helical track on the edge of a bowl....
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References
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Book•
01 Jul 1999
TL;DR: In this paper, the authors present a model for SI units based on uniform motion in a circular path of Satellites and a polygon of forces and force amd acceleration.
Abstract: Preface. Note On SI Units. 1. Statics. 2. Moment. Couple And Torque. 3. Polygon Of Forces Frameworks. 4. Friction. 5. Work And Power. 6. Machines. 7. Motion Velocity And Acceleration. 8. Force Amd Acceleration. 9. Momentum And Energy. 10. Uniform Motion In A Circular Path Satellites. 11. Stress And Strain. 12. Shear Force And Bending Moment. 13. Heat Engines. 14. Temperature And Heat. 15. Expansion And Compression Of Gases. 16. Fuels Combustion, Energy Release. 17. Steam. 18. Energy, Heat And Work. 19. Heat Exchangers Power Generation Emissions. 20. The Prime Mover. 21. Fluids. Index.
50 citations
TL;DR: In this paper, six lignes droites de la vitesse associee a la forme d'onde de vibration generalisee are represented by six vibratoires non sinusoidaux.
Abstract: Representation par six lignes droites de la vitesse associee a la forme d'onde de vibration generalisee. Definition de cinq facteurs de distorsion afin d'obtenir la forme optimale de l'onde de vibration et les conditions optimales de transport. Suggestion d'ameliorations dans le rendement des transporteurs d'alimentation vibratoires non sinusoidaux. Confirmation des resultats theoriques par des donnees experimentales
32 citations
01 Nov 1988
TL;DR: In this paper, the performance of a vibratory conveyor excited by two in-phase non-sinusoidal displacement cycles composed of the first two harmonics along the trough and perpendicular to it was investigated.
Abstract: A vibratory conveyor is essentially an inclined plane which is subjected to an acceleration cycle, conventionally sinusoidal. It is used to transport components or material. Usually rapid upward motion is desired. This paper presents the results of an investigation on the performance of a vibratory conveyor excited by two in-phase non-sinusoidal displacement cycles composed of the first two harmonics along the trough and perpendicular to it. Mean conveying velocity is found to be considerably larger than that of conventional vibratory conveyers if the proper amplitudes of the second harmonics are chosen.
24 citations
22 citations