# Comparison of crank based leg mechanism/Table
## Description

As mentioned before, the stride length is normalized to 1.00. The minimum foot position is defined as y=0. (so all coordinates have a positive y-value) The locus is vertically centred around x=0.
The lift off, is how much the foots lifts off from the ground during the stride. (here calculated as maximum foot position minus minimum foot position). There is no ideal lift off. Lifting off the foot to much is a waste of energy. If the foot is not lifted enough, the robot can not clear obstacles.
The height is pretty straight forward. If a mechanism is to high, it can not walk under bridges, into caves, be parked in a parking garage or shipped in a container.
The crank radius is also straight forward.
T1 and T3 are the turning points where the mechanism changes from transfer phase to support phase or support phase to transfer phase. T2 is (if existing) a local maxima.
The direction of rotation is straight forward as well. We let the mechanism walk left and see in which direction the crank turns.
The ratio of support to transfer phase is just that. A ratio of 1.00 would mean, that the transfer phase would need no time at all. This would be ideal on one hand, but impossible on the other. A ratio of 0.00 means virtually no support phase. A ratio of 0.50 is required when planing to use sets of two legs. A ratio of 0.33 is required when planing to use sets of three legs. Note that the simulation here only ran with 36 steps - the aquracy of the number shown here is there for limited to 1/36 (apprx. 0.03) For getting an idea, this is good enough, but please keep it in mind.
The circle is a bit of a joke, as the circle is simplest walking mechanism and has the simplest locus. The wheel can also be seen as a special case of walking mechanism. The stride length is infinitely small, so normalizing does not makes sense.
On the other hand: In some case, an elliptic motion has been suggested for certain application(s) for legged robots.

## Table

| * | stride length | lift off | height | crank radius | T1 | T1 | T2 | T2 | T3 | T3 | direction of rotation | Stride to transfer |
| * | stride length | lift off | height | crank radius | x | y | x | y | x | y | direction of rotation | Stride to transfer |
| extra simple walker | 1.000 | 0.651 | 2.117 | 0.382 | -0.5000 | 0.2181 | (-) | (-) | 0.5000 | 0.2181 | CW | 0.33 |
| Jansen | 1.000 | 0.329 | 1.852 | 0.221 | 0.5000 | 0.0488 | (-) | (-) | -0.5000 | 0.0481 | CCW | 0.63 |
| Klann 1 | 1.000 | 0.523 | 1.917 | 0.266 | -0.5000 | 0.0484 | -0.0923 | 0.0546 | 0.5000 | 0.0199 | CW | 0.47 |
| Klann 2 | 1.000 | 0.609 | 1.949 | 0.241 | -0.5000 | 0.0488 | -0.1006 | 0.0544 | 0.5000 | 0.0028 | CW | 0.44 |
| Ghassaei | 1.000 | 0.243 | 1.713 | 0.269 | 0.5000 | 0.0373 | (-) | (-) | -0.5000 | 0.0378 | CCW | 0.64 |
| Plantigrad Machine | 1.00 | 0.183 | 1.655 | 0.209 | -0.5000 | 0.0204 | -0.2599 | 0.0008 | 0.5000 | 0.0204 | CW | 0.67 |
| Circle | 0.000 | 1.000 | 1.000 | 0.500 | -0.500 | 0.500 | (-) | (-) | 0.500 | 0.500 | CCW | 0.00 |
| Grooved | 1.0000 | 0.2051 | 1.1337 | 0.4286 | ? | ? | ? | ? | ? | ? | ? | 0.5278 |
| TrotBot MainFoot | 1.0000 | 0.2696 | 1.5488 | 0.3262 | ? | ? | ? | ? | ? | ? | ? | 0.6111 |
| * | stride length | lift off | height | crank radius | T1 | T1 | T2 | T2 | T3 | T3 | direction of rotation | Stride to transfer |

## References

* 1 2 3 Shigley, Joseph E. “The Mechanics of Walking Vehicles: A Feasibility Study.” University of Michigan Department of Mechanical Engineering. 1960.
* ↑ A Locomotive Mechanism for a Robotic Colonoscope
* ↑ http://www.instructables.com/id/Extra-simple-walking-mechanism/