If you have a right-hand drive Cox Cheetah, it only means that the chassis is not from the kit of the RTR but from one of the chassis kits offered by the company for the TTX100 or TTX200 motors and the motor is not the correct one for the chassis. The kit and RTR only came with the TTX250 motor, and there were no variations. But a TTX200 with endbell-side drive can be mounted the wrong way and that would make the chassis a bit too wide.
You might also want to confirm that you're talking about the 1/24 sidewinder and not the 1/32 inline... My first reaction on hearing right-hand drive was to think about inline gear placement, but maybe i'm a linear thinker...
Just took a quick sampling of all my built-up Cox sidewinder cars: all left-hand drive, including the Cheetah, both regular and "team modified", except for the Ford GT40 that has the earlier model Cox motor with endbell drive.
The answer is simple: you have the wrong motor in the chassis. Your chassis is designed for the TTX200 endbell-side drive, and you have a TTX250 can-side drive in it, meaning that the drive is on the wrong side.
The motor for this chassis of yours MUST be a TTX200, a Russkit 33 or a Revell SP600, all early issues Mabuchi FT36 motors. The only FT36D motors that will fit (with the upgraded endbell and brushes) will be the K&B Bobcat (yellow motor with endbell-side drive).
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