There has been a growth in the design and use of power assist devices for manual wheelchairs (MWCs) to alleviate the physical load of MWC use. A pushrim-activated power-assisted wheel (PAPAW) is an example of a power assist device that replaces the conventional wheel of a MWC. Although the use of PAPAWs provides some benefits to MWC users, it can also cause difficulties in maneuvering the wheelchair. In this research, we examined the characteristics of wheelchair propulsion when using manual and powered wheels. We used the left and right wheels' angular velocity to calculate the linear and angular velocity of the wheelchair. Results of this analysis revealed that the powered wheel's controller is not optimally designed to reflect the intentions of a wheelchair user. To address some of the challenges with coordinating the pushes on PAPAWs, we proposed the design of a user-intention detection framework. We used the kinematic data of MWC experiments and tested six supervised learning algorithms to classify one of four movements: "not moving", "moving straight forward", "turning left", and "turning right". We found that all the classification algorithms determined the type of movement with high accuracy and low computation time. The proposed intention detection framework can be used in the design of learning-based controllers for PAPAWs that take into account the individualized characteristics of wheelchair users. Such a system may improve the experience of PAPAW users.