Rehabilitation aims to ameliorate deficits in motor control via intensive practice with the affected limb. Current strategies, such as one-on-one therapy done in rehabilitation centers, have limitations such as treatment frequency and intensity, cost and requirement of mobility. Thus, a promising strategy is home-based therapy that includes task specific exercises. However, traditional rehabilitation tasks may frustrate the patient due to their repetitive nature and may result in lack of motivation and poor rehabilitation. In this article, we propose the design and verification of an effective upper extremity rehabilitation game with a tangible robotic platform named Cellulo as a novel solution to these issues. We first describe the process of determining the design rationales to tune speed, accuracy and challenge. Then we detail our iterative participatory design process and test sessions conducted with the help of stroke, brachial plexus and cerebral palsy patients (18 in total) and 7 therapists in 4 different therapy centers. We present the initial quantitative results, which support several aspects of our design rationales and conclude with our future study plans.