Modeling and motion extraction of human upper limbs are essential for interpreting the natural behavior of upper limb. Owing to the high degrees of freedom (DOF) and highly dynamic nature, existing upper limb modeling methods have limited applications. This study proposes a generic modeling and motion extraction method, named Primitive-Based triangular body segment method (P-BTBS), which follows the physiology of upper limbs, allows high accuracy of motion angles, and describes upper-limb motions with high accuracy. For utilizing the upper-limb modular motion model, the motion angles and bones can be selected as per the research topics (The generic nature of the study targets). Additionally, P-BTBS is suitable in most scenarios for estimating spatial coordinates (The generic nature of equipment and technology). Experiments in continuous motions with seven DOFs and upper-limb motion description validated the excellent performance and robustness of P-BTBS in extracting motion information and describing upper-limb motions, respectively. P-BTBS provides a new perspective and mathematical tool for human understanding and exploration of upper-limb motions, which theoretically supports upper-limb research.