This article delineates the formulation and verification of an innovative robotic elbow-and-forearm system design, mirroring the intricate biomechanics of human musculoskeletal systems. Conventional robotic models often undervalue the substantial function of soft tissues, which provides a compromise between compactness, safety, stability, and range of motion. In contrast, this study proposes a holistic replication of biological joints, encompassing bones, cartilage, ligaments, and tendons, culminating in a biomimetic robot. The research underscores a compact and stable structure of the human elbow and forearm, attributable to a tri-bone framework and diverse soft tissues. The methodology involves exhaustive examinations of human anatomy, succeeded by a theoretical exploration of the contribution of soft tissues to the stability of a prototype robotic elbow-and-forearm system. Evaluation results unveil remarkable parallels in the range of motion between the robotic joints and their human counterparts. The robotic elbow emulates 98.8% of the biological elbow's range of motion, with high torque capacities of 11.25 N $\cdot$ m (extension) and 24 N $\cdot$ m (flexion). Similarly, the robotic forearm achieves 58.6% of the human forearm's rotational range, generating substantial output torques of 14 N $\cdot$ m (pronation) and 7.8 N $\cdot$ m (supination). Moreover, the prototype exhibits significant load-bearing abilities, resisting a 5 kg dumbbell load without substantial displacement. It demonstrates a payload capacity exceeding 4 kg and rapid action capabilities, such as lifting a 2 kg dumbbell at a speed of 0.74 Hz and striking a ping-pong ball at an end-effector speed of 3.2 m/s. This research underscores that a detailed biomechanics study can address existing robotic design obstacles, optimize performance and anthropomorphic resemblance, and reaffirm traditional anatomical principles.