Digitalized hand-drawn pattern is a noninvasive and reproducible assistive manner to obtain hand actions and motions for evaluating functional tremors and upper-limb movement disorders. In this study, spirals and straight lines in polar coordinates are used to extract polar expression features such as the key parameters deviation (cm) and accumulation angle (rad). These parameters are quantitative manner to scale the variations of functional tremors in normal control subjects and patients with Parkinson's disease (PD) and essential tremor (ET). However, difficulty arises in using nonlinear polar expression features in the two-dimensional feature space to separate normal control subjects from those with PD and ET. To solve the nonlinear separable classification problem, hash transformation is used to map polar expression features to a high-dimensional space using hash weighing function and modulo operation. Then, a machine learning method, such as the generalized regression neural network (GRNN), is implemented to train a decision-making classifier using the particle swarm optimization (PSO) algorithm for possible class assessment. With the enrolled data from 50 subjects, the fivefold cross validation, mean true positive, mean true negative, and mean hit rates of 98.93%, 98.96%, and 98.93%, respectively, are obtained to quantify the performance of the proposed decision-making classifier to identify normal controls and subjects with PD or ET. The experimental results indicate that the proposed screening model can improve the accuracy rate compared with the conventional machine learning classifier.