Physical activity recognition in patients with Parkinson's Disease (PwPD) is challenging due to the lack of large-enough and good quality motion data for PwPD. A common approach to this obstacle involves the use of models trained on better quality data from healthy patients. Models can struggle to generalize across these domains due to motor complications affecting the movement patterns in PwPD and differences in sensor axes orientations between data. In this paper, we investigated the generalizability of a deep convolutional neural network (CNN) model trained on a young, healthy population to PD, and the role of data augmentation on alleviating sensor position variability. We used two publicly available healthy datasets - PAMAP2 and MHEALTH. Both datasets had sensor placements on the chest, wrist, and ankle with 9 and 10 subjects, respectively. A private PD dataset was utilized as well. The proposed CNN model was trained on PAMAP2 in k-fold cross-validation based on the number of subjects, with and without data augmentation, and tested directly on MHEALTH and PD data. Without data augmentation, the trained model resulted in 48.16% accuracy on MHEALTH and 0% on the PD data when directly applied with no model adaptation techniques. With data augmentation, the accuracies improved to 87.43% and 44.78%, respectively, indicating that the method compensated for the potential sensor placement variations between data. Clinical Relevance- Wearable sensors and machine learning can provide important information about the activity level of PwPD. This information can be used by the treating physician to make appropriate clinical interventions such as rehabilitation to improve quality of life.