Parkinson's disease (PD), the second most common neurodegenerative disorder, is characterized by dopaminergic neuron loss and the accumulation of abnormal synuclein. PD presents both motor and non-motor symptoms that progressively impair daily functioning. The severity of these symptoms is typically assessed using the MDS-UPDRS rating scale, which is subjective and dependent on the physician's experience. Additionally, PD shares symptoms with other neurodegenerative diseases, such as progressive supranuclear palsy (PSP) and multiple system atrophy (MSA), complicating accurate diagnosis. To address these diagnostic challenges, we propose a machine learning-based system for differential diagnosis of PD, PSP, MSA, and healthy controls (HC). This system utilizes a kinematic feature-based hierarchical feature extraction and selection approach. Initially, 18 kinematic features are extracted, including two newly proposed features: Thumb-to-index vector velocity and acceleration, which provide insights into motor control patterns. In addition, 41 statistical features were extracted here from each kinematic feature, including some new approaches such as Average Absolute Change, Rhythm, Amplitude, Frequency, Standard Deviation of Frequency, and Slope. Feature selection is performed using One-way ANOVA to rank features, followed by Sequential Forward Floating Selection (SFFS) to identify the most relevant ones, aiming to reduce the computational complexity. The final feature set is used for classification, achieving a classification accuracy of 66.67% for each dataset and 88.89% for each patient, with particularly high performance for the MSA and HC groups using the SVM algorithm. This system shows potential as a rapid and accurate diagnostic tool in clinical practice, though further data collection and refinement are needed to enhance its reliability.