Traditional limb kinematic analysis relies on manual goniometer measurements. With computer vision advancements, integrating RGB cameras can minimize manual labor. Although deep learning-based cameras aim to offer the same ease as manual goniometers, previous approaches have prioritized accuracy over efficiency and cost on PC-based devices. Nevertheless, healthcare providers require a high-performance, low-cost, camera-based tool for assessing upper and lower limb range of motion (ROM). To address this, we propose a lightweight, fast, deep learning model to estimate a human pose and utilize predicted joints for limb ROM measurement. Furthermore, the proposed model is optimized for deployment on resource-constrained edge devices, balancing accuracy and the benefits of edge computing like cost-effectiveness and localized data processing. Our model uses a compact neural network architecture with 8-bit quantized parameters for enhanced memory efficiency and reduced latency. Evaluated on various upper and lower limb tasks, it runs 4.1 times faster and is 15.5 times smaller than a state-of-the-art model, achieving satisfactory ROM measurement accuracy and agreement with a goniometer. We also conduct an experiment on a Raspberry Pi, illustrating that the method can maintain accuracy while reducing equipment and energy costs. This result indicates the potential for deployment on other edge devices and provides the flexibility to adapt to various hardware environments, depending on diverse needs and resources.