Research and development efforts into small upper limb rehabilitation robots for home-based rehabilitation have been made in order to reduce the patient burden associated with making visits to the hospital. However, currently, there are only a few small upper limb rehabilitation robots capable of providing training that is tailored to account for the differences in individual patients. This is because many robots use omni wheels for their movement mechanism, thus causing problems when measuring patient motor function because it is not possible to accurately estimate the position. To solve this problem, in this study, we propose a new small upper limb rehabilitation robot that switches the driving unit from an omni wheel to an omnidirectional drive gear mechanism, as a mechanism that does not cause slips. Although an omnidirectional drive gear poses problems in terms of machining difficulty and weight, these problems can be solved by using a 3D printer. We show that position errors in small upper limb rehabilitation robots are greatly reduced by introducing a gear mechanism.