Collaborative robots or Co-robots are widely used in automation industries and material handling. Co-robots are designed to work with human workers side by side. However, safety is a challenging major concern. Rigidity is required to carry a payload and achieve accuracy in motion, while flexibility is often required for safe human interaction. Robots with control over their stiffness could combine some of the advantages seen in compliant robots with the performance of traditional rigid robots. This paper introduces the related research on variable stiffness robots and several variable stiffness solutions based on mechanical structures. These methods are classified based on the working principles and compared quantitatively based on the criteria such as stiffness range, stiffness ratio, and response time. Pros and cons are also described for each method. Researchers in design innovation and simulation laboratory also present several example applications of these variable stiffness mechanisms to collaborative robotic arms and grippers.