The official machines always had an oblique blade, but other shapes were used one guillotines homemade in the provinces, when the official guillotine was a long time comming.
The Guillotine has changed since it's first appearance in 1792. And the model shown here is my guess of how it may have looked. The original machine is not preserved, but there are guillotines in museums in Belgium, that looks a bit like this one. The correct time for this model may be between 1792 and 1795.

The biggest change and improvement was made by Leon Berger in 1870-72. The guillotine became more mobile and easier to mount.

New features were added, but the principle and the effect remained the same.

In 1792 the guillotine was made of red painted wood. A simple device on the side was used to maintain the blade/mouton in position, and to release it. The rope followed the mouton down.

The wooden grooves were very soon lined with brass or iron, to prevent the wood from swelling, which could interfere with the movement of the mouton. And the rope was no longer following the mouton down, which gave the mouton more speed.Two guillotines
In 1870 the vertical posts were supported by metal braces. The mouton was driving in the grooves on four wheels, two in each groove. On top it was held in place by an ingenious contraption, consisting of an arrow headed spike and a sprung-grab. The jaws of the sprung-grab were opened by means of a handle on the post. When the mouton was in position the rope was pulled of the hook by means of a thin rope. To stop the falling mouton, a spring-system was placed in the lower end of the grooves.

The lunette had a copper facing towards the side of the blade, and a new lock/release mechanism was implemented.