This paper highlights that while the integration of large-scale language models (LLMs) with robotic systems is advancing, it remains constrained by existing robot architectures, particularly serial mechanisms. This hardware dependency fundamentally limits the scope of robotic intelligence. To address this, we propose a framework called Intelligent Generative Robotic Design (INGRID). INGRID enables the automatic design of parallel robotic mechanisms using reciprocal screw theory and kinematic synthesis. It divides the design task into four steps: constraint analysis, kinematic joint generation, chain configuration, and complete mechanism design. INGRID generates novel parallel mechanisms with fixed and variable mobility and discovers kinematic configurations not previously documented in the literature. Through three case studies, we demonstrate how INGRID helps users design parallel robots for specific tasks based on their desired mobility requirements.