I made an axe mechanism for my robot Onyx a good few years ago. Started off with a drill motor powering it before switching to a scooter motor as the drill motor gearbox was too fragile. Here's a look at the transmission with the drill motor fitted:
onyx_build (1).jpg
It's a 5:1 ratio using 8mm 05B chain from Technobots. Think it's a 40T sprocket on the axe and a 8T one on the motor. Just drilled two holes in the axe arm and large sprockect to bolt them together, then drilled a central hole for the shaft, which was 12mm silver steel. It's a live shaft so I used grub screws tapped into the boss of the large sprocket to pin it to the shaft, and then there were 12mm needle roller bearings in either bulkhead (second bulkhead removed for visibility). Made for a very smooth mechanism.
I then switched to the scooter motor:
onyx_build (52).jpg onyx_build (53).jpg
It was a bit ungainly sticking out the back but it was a huge improvement. That just bolted to the baseplate with M6 bolts and again used an 8T sprocket. The only difference was that I welded the sprocket onto the shaft and got rid of the idler sprocket from the first picture as I managed to improve the chain tension. The axe arm was a section of hollow steel bar so I ran a steel cable from the axe head down to the shaft, round and back up to act as the tether, as specified by the rules.
And the mechanism in action:
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