Following PRISMA-ScR guidelines, this scoping review systematically maps the landscape of Large Language Models (LLMs) in mechanical engineering. A search of four major databases (Scopus, IEEE Xplore, ACM Digital Library, Web of Science) yielded 66 studies for analysis. The findings reveal a nascent, rapidly accelerating field, with over 68% of publications from 2024, and applications concentrated on front-end design processes like conceptual design and Computer-Aided Design (CAD) generation. The technological landscape is dominated by OpenAI's GPT-4 variants. A persistent challenge identified is weak spatial and geometric reasoning, shifting the primary research bottleneck from traditional data scarcity to inherent model limitations. This, alongside reliability concerns, forms the main barrier to deeper integration into engineering workflows. A consensus on future directions points to the need for specialized datasets, multimodal inputs to ground models in engineering realities, and robust, engineering-specific benchmarks. This review concludes that LLMs are currently best positioned as powerful 'co-pilots' for engineers rather than autonomous designers, providing an evidence-based roadmap for researchers, practitioners, and educators.