Klann linkage

About this Book
This wikibooks shall be a supplement to the Wikipedia article of the same name.

On Wikipedia, there is a need to compromise between readability, details and amount of illustration. It is impossible, to give an overview to the general public and an in depth view for engineers diving deeper into the topic at the same time.

So: Where the Wikipedia article brings a general overview, this book brings depth and details.

This book will also talk about the relevant patent(s). This book will shall not replace studying the patent, but simplifying it by providing additional tables and illustrations.

As the author of this book, I would like to cite larger sections of the patents. As the content of a patent may be copyrighted, this book will only cite small sections of the patent to be on the safe side.

A big thanks has to go to the patent holder Joseph Klann for his website, which is a great reference and for uploading pictures to Wikimedia Commons. Without the pictures from Joseph Klann on Commons and without his website, this book would not have been possible.

This book is the partner book to Comparison of crank based leg mechanism.

Parts
To get started, we look at the parts of the Klann Linkage, starting with a leg unit.

Leg Unit
First we take a look at this illustration:



In the patent, those parts are numbered as follow:

The supportive frame is of course simplified.

The axes/joints are named:



a pair of legs
Two leg units combine to form, as Mister Klann puts it, a wheel replacement.

The two units are one-half cycle out of phase (= 180 degree) to each other.

a full device
A full device consists of at least three pairs of legs, which means a total of six legs.

(see also https://web.archive.org/web/20170812223320/http://www.mechanicalspider.com/ for designs using the Klann linkage)

Geometry
Now we take a look at the "Enable diagram of Klann linkage" from Mister Klann:



How to construct it is described in the patent and on the website of the patent holder.

Our concern at the moment is how to interpret this drawing.

Points ending with "x" belong to the fully extended leg.

Points ending with "y" belong to the grounded gait position.

Points ending without a letter are fix points.

Points ending with "p" are auxiliary points used to construct the other points.

The suffix "c" is used for circles, "s" for straight lines and "a" are angles.

By "connecting the dots" without suffix, "x" suffix and "y" suffix, we can derive a first meaning from the drawing, showing us the frame and the leg in two positions.

examples
In the patent, there is are two tables with coordinates. Here we use those tables, but with the point description written next to it.

Table 1
(the table in the Wikipedia article is a cut down version of this table)

Table 2
(this table is omitted in the wikipedia article)

Input Variables
The geometric construction according to U.S. Patent 6,260,862 or more specifically the patent holders website has six input variables. We will consider the stride length as an input as well (here input 0), as table 2 uses bigger stride length. (notice that the same effect can be achieved by scaling all points and lengths proportionally)

An other thing to keep in mind is, that not all combinations of inputs result in a working linkage.

Table 1
The input variables for figure 17 (and therefore table 1) according U.S. Patent 6,260,862 are as follow: the values on the patent holders website for figure 2 are identical, but rounded

Notice that this set of values has some special properties: Therefore: Do not over generalize the drawing.
 * point 33x and 33y are both on circle 53c (which is not necessary as we see in table 2 from the patent)
 * line 67s and 51n overlap (which is caused by the -90 degree angle as input 4)

(if your colour blind: sorry for the heavy colour coding, but given the complexity of the drawing, I could not avoid to colour code the drawing)

Table 2
The input values for table 2 aren´t given in the patent on or the patent holders website, but can be reconstructed from table 2.

Notice that this set of values has some special properties: Therefore: Do not over generalize the drawing.
 * line 67s and 51n overlap (which is caused by the -90 degree angle as input 4)

Inputs
In this drawing, you see how the input variables influence the linkage:



Foot
An important part for a complete robot is the foot.

Inspiration for the foot can be found in the patent, Mondo spider Design and Theo Jansens Strandbeest Design.

Table 1
Presuming that the fasted foot defines the speed of the whole robot, we can animate a Robot based on the values in table 1:





It is a bit tricky to realize in the animation, but obvious in the graph: The robot comes to an almost stand still during each crank revolution.

Table 2
with the same assumption, we can also animate the robot according to table 2: