Posted by Oracid
(Editors note: you can see more of Oracid's inspiring creations here)

My goal is to explain simply how one can go from a usual 5 bars linkage to a 5 bars linkage with extension. The interest of this last mechanism is that it approaches the biological reality of a quadruped or a biped.

In Fig.1, I show the equivalence between a usual 5 bars and its diamond-shaped reduction.
The difference between these two linkages is located at the g bar which is fixed to the chassis. In the second linkage, the 5 bars turn into diamond with g = 0. Only the axis of rotation remains which fixes the 5 bars to the chassis.

​​In Fig.2, I show that the shape of the bar c1 does not matter, provided that its ends keep the same position.
For clarity, only the left side of the 5 bars is shown.

In Fig.3, I show that we can move part of the line c1, provided that the parts are connected by an articulated bar forming part of a parallelogram.
For clarity, only the left side of the 5 bars is shown.
Here is how to go from the assembly in Fig.3-1 to the assembly in Fig.3-2 by translating part of the line c1 and the line a1. Notice that point P remains at the same position.

​​In Fig.4, I show that whatever the angle of c1 with the horizontal in Fig.4-1 and Fig.4-3, there is respectively equivalence of the position of point P in Fig.4-2 and Fig.4-4.
It is as if the two parts of c1 are one. This is because a1 and c2 (not shown, here) form a parallelogram which keeps the two parts of c1 at the same angle.
For clarity, only the left side of the 5 bars is shown.

In Fig.5, we can see a summary of the translations of the bars c1 and a1.
The bar a1 is positioned at the end of the remaining part of the bar c1, while the “ghost” of the second part of c1 is translated and merged with a2.

Fig.6 shows the result of the transformation and the equivalence of the two mechanisms.

Also, check out Oracid's single DOF linkages, like this:

Posted by Wade
​As we learned during our attempt to scale up TrotBot, not all robot's legs will walk by pushing or pulling the robot. When we pushed TrotBot Ver 0 with its more rectangular-shaped footpath, the cranks would initially rotate, and then the linkage would freeze and the feet would skid on the pavement. Instead, we had to manually rotate TrotBot's cranks to make it walk:

The same thing happened when we tried to push our LEGO Klann walkers with the motors disengaged - the feet would skid and the cranks would not rotate. In both cases, this was due to the linkage being at a sort of reverse Dead-Point.

This behavior can be predicted from the image of Klann's linkage below.  Notice that when the crank is in such a horizontal position, all four feet are at the bottom corners of Klann's triangular foot-path.  Also notice that the feet slow to a virtual stop at these corners, as indicated by how bunched together the red dots are at the bottom corners of the foot-path.  In other words, rotating the crank +/- 10 degrees from this horizontal position would barely cause the feet to move. This also means that pushing the robot (and hence the feet) would not cause the feet to move nor the crank to rotate. Instead, it would only cause the legs to bend and the feet to skid, as happens with our prototypes.

This behavior is also indicated by linked bars being parallel - notice in the image above that the legs' connections to the crank are parallel with the crank, a tell-tale sign of a Dead-Point.

Below the crank has been rotated past this dead point where crank rotation causes foot movement and vice versa:

If another pair of legs were added to each side of Klann, as done in the simulation of Strider below, then maybe its legs could be driven by pushing the robot (although one of Klann's feet would still skid at the corner of the foot-path, so it may not work so well - maybe adding feet that could slide or rotate a little would help?)

Here's a test to see how easily this linkage variation #6 of Strider's mechanism can be driven by an external force - gravity in this case:

​Notice how the robot wavers slightly to the left and right as it descends, due to the foot-speed varying a little.  Linkage variation 7 below has more consistent foot speed, and waivers less

​Passive walking can also be tested by pulling the robot with a rope:

Strider's legs can also be driven by pushing the robot when built in an 8-leg version, although not nearly as efficiently as 12-leg versions, and the ramp's slope had to be increased to get an 8-legged Strider to walk below:

​Dead-Points part 1 is here.