CONCEPT
LINKAGE.WMV

THEO JANSEN
A single leg consists of a six-bar 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 straight-line portion of the path traced by the foot. The result of two of these linkages coupled together at the crank and one-half 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, mid-stride, 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 stilt-walker 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 JAVA-Challenged:
SPIDER HOME , CONCEPT , MOTION , ENABLE TEXT , US PAT. 6,260,862 , US PAT. 6,364,040 , US PAT. 6,478,314

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