Peaucellier Linear Linkage for Vex Round Up

I am trying to revive the Grant HS Vex robotics team.   I helped start this team several years ago but they lost their mentor this year and got off to a late start.   I worked with them during the first four days of their winter break.   We are going to try a Peaucellier linear linkage to make the lift go vertical.

Peaucellier’s linkage
http://web.mat.bham.ac.uk/C.J.Sangwin/howroundcom/straightline/exact.html
http://en.wikipedia.org/wiki/Peaucellier%E2%80%93Lipkin_linkage
Should be fun if it works and doesn’t weigh too much.
The actual design marries a 7 bar desk lamp (Two  4 bars in series  with a common middle link) and Peaucelliers linkage.   The top two linkages of Peaucelliers are in common with the bottom two linkages of the 7 bar.   The 7 bar provides the strength structures and torque while the Peaucellier provides the guide to maintain the vertical movement.  In total there are  7 plus 5 or 12 linkage bars.    All linkages are dual with about 3 inches separation to provide lateral stability.
We have the preliminary design prototyped and it gives an 18 in delta vertical movement.

Preliminary Torque Requirements:

The plan is to drive it as one would a standard 4 bar.  This has the advantage that if it doesn’t pan out, it can easily be converted to a 4 bar design without major structural changes.    I haven’t done a force analysis, but I am guessing that this design requires more torque than an equivalent 4 bar with the same length as the distance between the rear pivot and the back of the claw when the claw is at mid position.

One can estimate the average torque by using a virtual work analysis.   Work done by the arm is equal to the work of lifting the load.

τ*Δθ = W*Δh  where

Δθ is the angle the torqued bar changes (rad) ,

Δh is the corresponding change in the claw height (in)

τ is the torque (in_lbs)

W is the equivalent weight lifted (lbs)…. we add a little extra here for the lift structure and assume it is lifted the whole  height.

Δh = 18 in,

Δθ = ∏/2 = 1.57 (90 degrees)

W = 3 lbs   (1 lb for claw, 1 lb for tubes and 1 lb for the linkage)

τ = 3*18/1.57 = 34.4 in_lbs  ….  With a 50% safety margin, we should design for around 50 in_lbs.

If we operate with a 5:1 gearing, then we need 10 in_lbs from the motors and any elastic bands used to help neutralize the lift load.

Lets look at using  big 393 motors … each can supply a max torque of 13.5 in_lbs and a static friction hold of 1 in_lb.  With 2 motors we get 27 inlb of max torque and 2 in_lbs of friction torque.

So to hold the lift in position we need a net of 10 – 2 = 8 in_lbs of torque, which without elastic represents about 30% of max torque.  This will overheat the motors in the course of a match.  So   we need  to cut this down to about 15% (4 in_lbs) of max torque if the motors are going to continuously hold the torque during a match.

One way would be to add two extra legacy motors to provide extra friction and max torque capability and the other might be to add elastic tension to the inner pivot bar used in the Peaucellier linkage set.   We could tie rubber tubing  to the point where the pivot bar attaches to the Peaucellier cage and stretch it to the upper back of the robot creating enough force to hold the lift in the center position without motor input.      Anyway, some experimentation is in order.

More later.

1/5/11 Update: To simplify the motor selection the following rules of thumb could be applied if motors are to hold continuous torque to counter gravity.

393 motors: 1 in_lb static, 2 in_lbs dynamic(15% max torque) … total 3 in_lbs

legacy 3 wire: .6 in lbs static, 1 in_lbs dynamic (15% max torque) .. total 1.6 in_lbs

So… we need 10 in_lbs total.   2 393’s and 2 legacy gives  3+3+1.6+1.6= 9.2 in_lbs.

That leaves a requirement for 1 in_lb of elastic torque and a steady state drain of current = 15%*total max current = .15*(3.6+3.6+1.6 +1.6) = 1.6 amps

This creates a battery drain equivalent to one legacy motor running stalled.

To have minimum current draw, we would need  10 – 3.4 = 6.6 in lbs of elastic torque to augment just the static friction of the motors.

If we are willing to trade speed for less torque… say using 7:1 gearing then 2 393 motors might suffice .

Update 7/1/2012 More recent blog links:

Team 1508a Lancers Compete Peaucellier Design at 2011 Vex Round Up World Championships

Team 1508a Vex Peaucellier Lift Roundup Youtube Video

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