Brain Teaser Challenge Solution - March 2004

Butch Shadwell

Several readers have already sent in answers to the last BTC, all were correct. The West Indian robotic problem went like this, “a little machine that was driven by two large wheels on either side, and a third idler wheel in the back that kept it stable. Each wheel could be advanced one thousandth of a turn for each pulse it was fed, and the drive wheels were 5 inches in diameter and mounted 10 inches apart. …the count totalizer for each wheel showed the right wheel had been fed 1,000,000 counts and the left wheel had been fed 638,000 counts, all in the forward direction. If the robot was facing north (0 degrees on the compass) when it started these maneuvers, what direction was it facing when they ended? Assume there was no slippage of the drive wheels and that they had very small contact surfaces with the ground.” Nigel wasn’t his real name.

The simplest solution is to determine the difference and direction of thepulse count and then advance the higher count wheel alone to that degree. So we determine that the right has moved forward 362,000 counts. At 1000 counts per revolution, that means that the right wheel has advanced 362 turns more than the left one. Since the wheel spacing is 10”, the circumference of a full turn (2*pi radians) is pi*20”. One full turn of a wheel covers pi*5”. From this we know that 4 revolutions of one wheel, more than the opposite wheel, will take the robot full circle. Dividing 362 by 4, we get 90.5 complete circles by our machine. The last half circle means that the robot must be facing South at the end of the course. But I bet you already knew that.

Brain Teaser Challenge - June 2004

Butch Shadwell

One of the most fun things I have ever done is design some robotic control systems for an amusement park in northern England. In the mid 80’s I spent some time there installing these systems, and the robotic characters, at Alton Towers, located near Stafford, England. I got to install “Henry the Hound of the Towers” at the entrance promenade. Henry was a hound dog that stood about seven feet tall. It was very interesting to watch them building this world class amusement park from scratch.

While working there, I stayed at a B&B that was owned by a professional chef. The food was great, and I always enjoyed a little conversation with the other guests and owners in the evening. My wife and I have really enjoyed traveling around Great Britain and staying at B&Bs. We’ve once stayedat a Scottish castle, and in some beautiful farm country too. But I digress.

Henry was a pneumatically actuated character. That is, all of his joints were operated by air pistons. The elbow used a 1” cylinder to move his forelimb out and in again. This cylinder had a ¼” piston rod. Henry’s arm extended just fine but would hesitate while retracting. The arm retraction was powered by the cylinder’s retraction motion, as opposed to the extension motion. With a 90 pound air supply, how much force was the cylinder applying to the retraction function?

Reply to Butch Shadwell at (email), 904-223-4510 (fax), 904-223-4465 (v), 3308 Queen Palm Dr., Jacksonville, FL 32250-2328. ( The names of correct respondents may be mentioned in the solution column.

IEEE Region 3 eNewsletter Volume 19 No. 4, August 2004, © 2004 IEEE
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