<p>This study investigates a predefined-time control approach for a class of <i>n</i>-link robotic systems with unknown nonlinearities. First, a time-varying scaling transformation is designed to drive the tracking errors into an adjustable range within a predefined time. Then, a novel nonsingular fast predefined-time sliding mode surface is used to develop a predefined-time controller. By introducing a simple variable-exponent coefficient in the sliding variable, the control method can achieve the prescribed performance without encountering singularities. Specifically, both transient and steady-state performances are ensured under a weaker excitation condition known as interval excitation, thereby relaxing the system’s excitation requirements. Building on this, a new predefined-time parameter composite learning law is constructed by fully leveraging the information from parameter estimation errors and system tracking errors. Coupled with the predefined-time strategy, the concise relationship between the tuning gains and the predefined stabilization time is established. Theoretical analysis and experimental results confirm the proposed controller’s superior performance in parameter estimation and trajectory tracking.</p>