Compliant mechanisms have been widely used in various mechatronics and robotics applications as they offer several significant advantages like repeatability and non-existence of backlash. The designs of these compliant mechanisms are often based on experience and intuition, and can be a frustrating experience during the design phase. Hence, this paper proposes an algorithm that aids users in designing compliant mechanisms for torsional applications in a systematic manner. With the proposed algorithm, users can input the desired torque-angular displacement stiffness property into the proposed algorithm, and the algorithm will output an appropriate compliant mechanism design accordingly. In this paper, two scenarios are explored, namely: 1) robotic arm with minimal impedance due to its own mass so as to reduce the required motor size, and 2) desired resonant frequency for better control or energy harvesting purposes. These two scenarios are used as motivation to input the required information to the algorithm, which generates the appropriate solution of compliant mechanism designs to address the need of the scenarios. Prototypes are developed for the above mentioned scenarios, and experiments are conducted to demonstrate the performance of the proposed algorithm.