Essential tremor (ET) is one of the most common neurological disorders, and its mainly clinical symptoms, including patient hand's kinetic tremor, dystonia, ataxia, etc., would influence the daily life of patients inordinately. Current ET diagnosis highly replies on the clinical evaluation and neurological examination, so the objective measurement indicators are particularly important in the auxiliary diagnosis of ET. In this research, the Archimedes spiral line freehand sketching samples without template assistance is collected and the Convolutional Neural Network (CNN) model of optimized structure is adopted to fully analyze the tremor, spacing of turns, shape, etc. shown in the handwriting samples of patients with ET, including the following main process: characteristics extraction, model visualization and subregional relevance evaluation. Dropout is used as a regularization technique in the network structure. The test group consisted of 50 patients with confirmed ET and the control group consisted of 40 healthy individuals. The main research objectives of this paper comprise two points: on the one hand, to achieve effective automatic classification of patients with ET and healthy controls using a scheme combining deep learning and simple hand mapping for the purpose of primary disease screening; on the other hand, to design sub-regional automatic classification experiments to demonstrate that Archimedean spiral hand drawings of patients with ET do have distinct local features, and to lay the experimental foundation for future hand drawing-based automatic aid for the identification of a variety of neurodegenerative diseases. Our model's average accuracy rate in test set reaches 89.3%, and average AUC is 0.972, with favorable stability and generalization performance. Besides, subregional characteristics recognition proofs that the spiral line samples of most of the patients with ET show more category-related characteristics in the local area of upper right, which provides evidences and theory update for predecessors' medical research.