Bowtie
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Here we present an example of the generic type of parallel manipulation achievable with the Universal Parts Manipulator (UPM): 3 pennies are placed on the device, equally spaced along a figure-eight curve (the "bowtie"). The intent is to have all coins flow simultaneously along this curve, thus proving that a clearly non-rigid, coordinated rearrangement of several objects in the plane is possible. 

The image below is what the system sees thru its overhead camera at the starting point of execution: the coins are the dark disks labeled 0, 1, 2; they are placed on the bowtie path at 2p/3 intervals; this distance is to be preserved during the motion. 

A control loop is run which routes all three coins simultaneously along the bowtie curve. This illustrates how the UPM, a 3-dof device, can be used to manipulate a system with a higher number of dof's (6 in this case).

Pictures of the motion are shown below; each combines 3 consecutive snapshots taken at regular intervals. Coins are identified by a number (0,1,2); displacement arrows indicate their displacement.

bowtie-abc.PNG (177284 bytes) bowtie-cde.PNG (177518 bytes)
bowtie-efg.PNG (177446 bytes) bowtie-ghi.PNG (176737 bytes)

Several snapshots are superimposed below showing the bowtie-curve traced by the 3 coins.

A movie of this curious motion, as it is physically executed by the UPM, is available below: 

Filmed by external camera
Real Video 8.0: [requires Real Player 8.0!]: 
high-bandwidth and low-bandwidth 
MPEG: download it!
Filmed by overhead camera
Real Video 8.0: [requires Real Player 8.0!]: 
high-bandwidth and low-bandwidth  
MPEG: download it!

Also: pictures of the UPM are available here; videos of the motion primitives used in this demo are available here.

 
2000 Dan S. Reznik, <dreznik@cs.berkeley.edu>