I have this 3-wheel robot for clearing snow. Problem is the front wheel in pic (which swivels) turns all the way and the robot locks i.e. can't move. Any ideas appreciated.

 

Is that wheel powered? If your saying it swivels it sounds like it's a caster, or should be. A caster is supposed to swivel. What is keeping it from going completely in 360 degrees? I one of the mounting bolts stopping it?
https://en.wikipedia.org/wiki/Caster

In a three wheel thing like that the steering should come from the independently driven rear wheels. Something called differential steering. https://en.wikipedia.org/wiki/Differential_steering

 

I have this 3-wheel robot for clearing snow. Problem is the front wheel in pic (which swivels) turns all the way and the robot locks i.e. can't move. Any ideas appreciated.

In this pic, the coupling between the gearbox and the wheels keeps on slipping. From the pic, the wheels are connected to a 3/4 " dia steel pipe and the gearbo has a square-threaded shaft. The coupling is of Al and has 2 threaded holes ones for the steel pipe, one for the threaded shaft. The screws keep on slipping on the shaft. Any ideas to solve this?

 

Hi B,
It appears that the front wheel swivels centrally, but it should be a trailing Castor, see attached.
C

 

In this pic, the coupling between the gearbox and the wheels keeps on slipping. From the pic, the wheels are connected to a 3/4 " dia steel pipe and the gearbo has a square-threaded shaft. The coupling is of Al and has 2 threaded holes ones for the steel pipe, one for the threaded shaft. The screws keep on slipping on the shaft. Any ideas to solve this?

This is purely mechanical. Slide on the coupling and use a marker to place a mark in the threaded hole for the set screw when the coupling is in the correct alignment.

Remove the coupling. With a drill bit the diameter of the set screw, drill a small depression for the set screw to land in. This depression will prevent the shaft from sliding.

I also recommend LocTite Blue on the set screws to minimize the chance of them loosening by vibration.

 

If you are moving snow that very small caster will become lodged in it. Consider a pair of small fixed skis mounted on the front with both ends curved pointing up so that you can reverse. I you must have a wheel it will need to be bigger so it can ride on the snow instead digging into it.