Here, an automatic design method for a serial link mechanism is proposed. This method outputs all kinematic parameters of joints, position, orientation, number, and type of joint (revolute or prismatic). Several studies have been conducted on optimizing only the positions and directions of joints for a desired path. However, automatically determining the numbers and types of joints requires an excessive calculation time owing to the complicity of kinematics. To handle heavy computation, a virtual screw joint (VSJ) is introduced based on a screw axis and the product of exponentials formula. Screw joints have the advantage of including both rotation and translation. First, an additional joint is optimized as a VSJ. Then, adopting its position and orientation and selecting a revolute or prismatic joint facilitate an efficient design process. To demonstrate the effectiveness of this study, two task motions addressed in a related work are adopted as target paths. Consequently, the proposed method automatically generates serial linkages that contain both revolute and prismatic joints and can follow along desired paths.

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