A steering system comprising: a first gear pair (81, 81A) that controls the turning of a non-driving wheel, the first gear pair including a non-circular drive gear (52, 52A) that engages a non-circular driven gear (70, 70A); a second gear pair (81, 81A) that controls the turning of another non-driving wheel, the second gear pair including a non-circular drive gear (52, 52A) that engages a non-circular driven gear (70, 70A); where the steering system is in a vehicle having a pair of drive wheels driven by a transmission system capable of driving the drive wheels at different speeds and in different directions, the transmission system is capable of causing the drive wheels to produce a first vehicle turn radius, and the first and second gear pairs are configured to cause the non-driving wheels to produce a second vehicle turn radius equal to the first vehicle turn radius for a given steering input, the transmission system including two independent drive units, one coupled to each drive wheel, the vehicle further comprising: a speed input device configured to be manipulated by an operator and two speed cams (112, 112A) coupled to the speed input device, each speed cam including a curved slot (119, 119A), the curved slots having the same shape, where movement of the speed input device causes the speed cams to rotate in the same direction and by the same amount about an axis extending through each of the curved slots; and a follower (120, 120A) riding in each curved slot, each follower coupled to one of the two drive units. a first gear pair (81, 81A) that controls the turning of a non-driving wheel, the first gear pair including a non-circular drive gear (52, 52A) that engages a non-circular driven gear (70, 70A); a second gear pair (81, 81A) that controls the turning of another non-driving wheel, the second gear pair including a non-circular drive gear (52, 52A) that engages a non-circular driven gear (70, 70A); where the steering system is in a vehicle having a pair of drive wheels driven by a transmission system capable of driving the drive wheels at different speeds and in different directions, the transmission system is capable of causing the drive wheels to produce a first vehicle turn radius, and the first and second gear pairs are configured to cause the non-driving wheels to produce a second vehicle turn radius equal to the first vehicle turn radius for a given steering input, the transmission system including two independent drive units, one coupled to each drive wheel, the vehicle further comprising: a speed input device configured to be manipulated by an operator and two speed cams (112, 112A) coupled to the speed input device, each speed cam including a curved slot (119, 119A), the curved slots having the same shape, where movement of the speed input device causes the speed cams to rotate in the same direction and by the same amount about an axis extending through each of the curved slots; and a follower (120, 120A) riding in each curved slot, each follower coupled to one of the two drive units. a speed input device configured to be manipulated by an operator and two speed cams (112, 112A) coupled to the speed input device, each speed cam including a curved slot (119, 119A), the curved slots having the same shape, where movement of the speed input device causes the speed cams to rotate in the same direction and by the same amount about an axis extending through each of the curved slots; and a follower (120, 120A) riding in each curved slot, each follower coupled to one of the two drive units.