Exploring human hand fundamental biomechanical features and exploiting them to robotic hands have been proven to be an effective approach to enhancing artificial hands' performance, especially when interacting with various objects in dynamic unstructured environments. In this article, a bioinspired anthropomorphic robotic finger is first proposed, which embeds human finger musculoskeletal features in the design. Based on this design, three human-finger-like biomechanical advantages are systematically investigated and embodied in the bioinspired robotic finger. This article for the first time derives, presents, and experimentally verifies the mathematical models for the variable stiffness of finger ligamentous joints and self-adaptive morphing mechanism of finger flexible tendon sheaths, and validates and compares the influence of the reticular and linear extensor morphologies on fingertip feasible forces in three-dimensional (3-D) space. In this Part I of the article, two of the biomechanical properties, i.e., joint stiffness generated by the ligamentous joint of the finger, and fingertip feasible force space influenced by the reticular extensor mechanism are systematically investigated through theoretical modeling and experimental verification. Correspondingly, two biomechanical advantages were found, i.e., the ligamentous joint of the finger could provide anisotropic variable joint stiffness, enhancing the adaptivity, dexterity, and stability of fingers; and a reticular extensor mechanism could enlarge the fingertip feasible force space in 3-D space by 30.9% theoretically and 146.4% experimentally on average compared with the linear extensor, contributing to enrich force conditions during interactions. The third biomechanical advantage, i.e., fingertip force–velocity workspace can be augmented through the flexible tendon sheath, and grasping tests for a robotic hand designed with the aforementioned advantages are presented in Part II of this article.