This device consists largely of 3 pieces. The piece that initiates the motion is a disk with a pin attached to it. The pin fits into a slot along a rod with about a quarter of a gear attached to the end of it. This piece rotates around a fixed point where the rod meets the gear. The gear then fits into a rectangular piece with teeth. As the the disk spins, the pin moves the rod to the left and right, and the the gear then move the rectangular piece back and forth.
When the rectangular piece is moving to the left, the pin is in the lowest position on the disk, so it is applying the force on the rod close to its axis of rotation. The location of the force causes the rod, gear, and therefore the rectangular piece to move more quickly. When the pin is closer to the top of the disk (when the rectangular piece is moving to the right), the force is being applied on the rod further away from the axis of rotation, which moves the rod, gear, and therefore rectangular piece, more slowly.
This mechanism could be useful if you needed to repeatedly apply a sharp force in one spot, but at a slower pace than if the rectangular piece was moving in both directions with the same speed, possibly to hammer something. I thought this mechanism was interesting because it has a fairly simplistic design, but it changes its motion so drastically. The initial movement is rotation with a constant velocity, but the device turns it into linear motion that changes both its direction and speed.
http://507movements.com/mm_131.html
I too thought this design was interesting because of the change in the linear velocity of the beam at the bottom. I was wondering what would the movement look like if the disk had a different shape and the crank moved differently. Maybe a rectangle or a triangle or an oval?