Lecturers of Engineering courses around the world are struggling to increase the engagement of students through the introduction of appropriate hands-on activities and assignments. In Biomechatronics and Robotics courses these assignments typically focus on how certain devices are designed, modelled, fabricated, or controlled. The hardware for these assignments is usually purchased by some external vendor and the students only get the chance to analyze it or program it, so as to execute a useful task (e.g., programming mobile robots to perform path following tasks). Student engagement can be increased by instructing the students to prepare the hardware for their assignment. This also increases the sense of ownership of the project outcomes. In this paper, we present how a robotic gripper / hand design project and the introduction of a grasping and manipulation competition as a course assignment, can significantly increase the student engagement and their understanding of the taught concepts. The presented best practices have been trialed over the last four years in two different courses (one undergraduate and one postgraduate) of the Department of Mechanical Engineering at the University of Auckland in New Zealand. For the particular assignment the students were asked to fully develop a robotic gripper or hand from scratch using a single actuator (only the actuator and the power electronics were provided). The performance of the developed devices was assessed through the participation in the grasping and manipulation competition. All the details of the proposed assignment are presented, hoping that they could help other lecturers and teachers to prepare similar activities.