Comments

1. 
   Filtersmith | May 21, 2015 03:46am | #1

   It's worth mentioning that the shape of the exponential (Bernoulli) spiral has a particular property useful for this application. To wit, there is a constant amount of squeeze applied for a given (small) motion of the clamped board, regardless of what the opening is. The spiral is given as r = r_0 * exp(k*theta), with theta given in radians and r_0 being the starting radius. Small k gives a slowly growing spiral, and large k gives a fast growing spiral.

   To calculate your own spiral, here's an expression to run in Excel. Adjust r_0 and k to suit your own table's separation of holes and how hard you want to squeeze (smaller k is harder squeeze but less clamp range).

   =$B$2*EXP($B$1*A7*PI()/180)

   where k is stored in B1, r_0 in B2, and column A has the angles in degrees. Here's an example:

   k = 0.6
   r_0 = 1

   Implements r = r_0 exp(k*theta*pi/180)

   angle (deg) radius
   0 1.0000
   5 1.0538
   10 1.1104
   15 1.1701
   20 1.2330
   25 1.2993
   30 1.3691
   35 1.4427
   40 1.5203
   45 1.6020
   50 1.6881
   55 1.7788
   60 1.8745
   65 1.9752
   70 2.0814
   75 2.1933
   80 2.3112
   85 2.4354
   90 2.5663