Efficacious stroke rehabilitation depends not only on patients' medical treatment but also on their motivation and engagement during rehabilitation exercises. Although traditional rehabilitation exercises are often mundane, technology-assisted upper-limb robotic training can provide engaging and task-oriented training in a natural environment. The factors that influence engagement, however, are not fully understood. This paper therefore studies the relationship between engagement and muscle activities as well as the influencing factors of engagement. To this end, an experiment was conducted using a robotic upper limb rehabilitation system with healthy individuals in three training exercises: (a) a traditional exercise, which is typically used for training the grasping function, (b) a tracking exercise, currently used in robot-assisted stroke patient rehabilitation for fine motor movement, and (c) a video game exercise, which is a proliferating approach of robot-assisted rehabilitation enabling high-level active engagement of stroke patients. These exercises differ not only in the characteristics of the motion that they use but also in their method of triggering engagement. To measure the level of engagement, we used facial expressions, motion analysis of the arm movements, and electromyography. The results show that (a) the video game exercise could engage the participants for a longer period than the other two exercises, (b) the engagement level decreased when the participants became too familiar with the exercises, and (c) analysis of normalized root mean square in electromyographic data indicated that muscle activities were more intense when the participants are engaged. This study shows that several sub-factors on engagement, such as versatility of feedback, cognitive tasks, and competitiveness, may influence engagement more than the others. To maintain a high level of engagement, the rehabilitation system needs to be adaptive, providing different exercises to engage the participants.