

LINKAGE.WMV
THEO JANSEN

A single leg consists of a sixbar linkage made up entirely of pivot joints that converts rotating motion into linear motion. One hundred and eighty degrees of the input crank results in the straightline portion of the path traced by the foot.
The result of two of these linkages coupled together at the crank and onehalf cycle out
of phase with each other is a device that can replace a wheel and allow the frame of the vehicle to travel relatively parallel to the ground. The remaining rotation of the input crank allows the foot to be raised to a predetermined height before returning to the starting position and repeating the cycle.
These figures show a single linkage in the fully extended, midstride, retracted, and lifted positions of the walking cycle. These four figures show the crank (rightmost link in the first figure on the left with the extended pin) in the 0, 90, 180, and 270 degree positions.
The three U.S. patents with figures that pertain to this linkage can be viewed by clicking the buttons on the left.


These are a few example inputs and the resulting coupler curves as described by the relationships in the enable text of the Klann linkage. The inputs and resulting outputs are displayed in the tables next to each graph. The yellow curves trace out the path of each of the points through one complete revolution of the crank. The dimensions are unitless as the linkage is entirely mechanical and can be scaled up or down. Animated gif files of each case can be viewed in a new window by clicking the link below the tables.
Enable001 – These inputs are the ones used in the four figures above and shown in figure 2 of the enable text.

Input 1  52p  50s  0.866 
Input 2  Rad 53c  1.000 
Input 3  Angle 9  30.000 
Input 4  Angle 65p  90.000 
Input 5  74p  75p  1.099 
Input 6  27x  29x  0.590 
Output  Step Height  52.3% 
Output  Deviation  5.5% 
Output  Stride  1.000 
Enable001 Animated GIF

Enable002 – This is one possible combination to get an almost straight line. The foot travels back and forth for 1.000 units for each complete revolution of the crank and deviates from a mathematically straight line by plus 0.003 and minus 0.001 units. It has no real step height and no value as a walking linkage but there were two people that found it interesting, me and one of my brothers. He was probably just being polite…

Input 1  52p  50s  2.500 
Input 2  Rad 53c  1.000 
Input 3  Angle 9  75.000 
Input 4  Angle 65p  90.000 
Input 5  74p  75p  1.500 
Input 6  27x  29x  1.500 
Output  Step Height  0.4% 
Output  Deviation  0.4% 
Output  Stride  1.000 
Enable002 Animated GIF

Enable003 – A special case where the ground points from the upper and lower rockers (point 9 and point 11) coincide to reduce the frame to a single line. There are other combinations of inputs where this happens but with six input variables there are quite a few possibilities and no real practical value in finding them.

Input 1  52p  50s  1.500 
Input 2  Rad 53c  1.000 
Input 3  Angle 9  20.100 
Input 4  Angle 65p  90.000 
Input 5  74p  75p  1.500 
Input 6  27x  29x  0.560 
Output  Step Height  89.8% 
Output  Deviation  6.3% 
Output  Stride  1.000 
Enable003 Animated GIF

Enable004  This combination of inputs yields a stiltwalker of sorts. Not recommended for going down steep inclines, although it is amusing to imagine someone trying…

Input 1  52p  50s  2.750 
Input 2  Rad 53c  1.000 
Input 3  Angle 9  45.000 
Input 4  Angle 65p  75.000 
Input 5  74p  75p  1.140 
Input 6  27x  29x  0.800 
Output  Step Height  22.8% 
Output  Deviation  2.2% 
Output  Stride  1.000 
Enable004 Animated GIF

Enable005 

Input 1  52p  50s  1.000 
Input 2  Rad 53c  0.750 
Input 3  Angle 9  5.000 
Input 4  Angle 65p  90.000 
Input 5  74p  75p  1.250 
Input 6  27x  29x  0.750 
Output  Step Height  40.2% 
Output  Deviation  3.8% 
Output  Stride  1.000 
Enable005 Animated GIF

Enable006  These inputs provide a more aggressive step height and reduce the dwell at the beginning and end of each stride.

Input 1  52p  50s  1.250 
Input 2  Rad 53c  1.500 
Input 3  Angle 9  15.000 
Input 4  Angle 65p  90.000 
Input 5  74p  75p  1.400 
Input 6  27x  29x  0.600 
Output  Step Height  76.0% 
Output  Deviation  6.8% 
Output  Stride  1.000 
Enable006 Animated GIF

Enable007  Exaggerated step height  Any walker with less and you might as well use a wheel.

Input 1  52p  50s  1.000 
Input 2  Rad 53c  1.100 
Input 3  Angle 9  20.000 
Input 4  Angle 65p  85.000 
Input 5  74p  75p  1.500 
Input 6  27x  29x  0.450 
Output  Step Height  183.6% 
Output  Deviation  9.3% 
Output  Stride  1.000 
Enable007 Animated GIF

Enable008  Stretched

Input 1  52p  50s  1.000 
Input 2  Rad 53c  1.000 
Input 3  Angle 9  10.000 
Input 4  Angle 65p  90.000 
Input 5  74p  75p  2.000 
Input 6  27x  29x  1.250 
Output  Step Height  36.7% 
Output  Deviation  3.4% 
Output  Stride  1.000 
Enable008 Animated GIF


Functions for the JAVAChallenged:
SPIDER HOME
,
CONCEPT
,
MOTION
,
ENABLE TEXT
,
US PAT. 6,260,862
,
US PAT. 6,364,040
,
US PAT. 6,478,314

© 2009 Klann R & D, LLC All rights reserved

