Many wheelchair users, such as the elderly or children with Profound Intellectual and Multiple Disabilities (PIMD), rely on a caregiver to push them. The lack of eye contact between the wheelchair user and caregiver hinders communication and can even be dangerous, for example for children with epilepsy. Conventional wheelchairs place the caregiver behind the patient when pushing the wheelchair, but this position obstructs communication and makes it harder to assess the user's health.

To facilitate face-to-face communication while walking, Lucy Bennett recently proposed a steering compensation method at BME2021 using a banked castor wheel to allow the caregiver to walk next to the wheelchair. This thesis contains a mathematical model for a castor wheel to determine how the three-dimensional orientation of the castor swivel axis and wheel spin axis, and external parameters such as rolling resistance affect the steering compensation. Both the Lagrange and virtual power methods are used to find the equations of motion of the castor wheel.

The steering effect was quantified as the moment generated by the wheelchair around its center of mass in the up direction. The cant angle of the castor wheel has the strongest steering effect. In the future, the developed mathematical model can be applied to calculate the influence of design variables to build a better prototype.