This study presents novel analysis and synthesis methods for a certain type of geared adjustable stroke mechanism. The mechanism has significance in mechanical design, as it has been used in practice. However, to the best of our knowledge, any theory on its analysis or synthesis is not available in the literature. The problem is divided into four parts and each part is generalized. Novel synthesis procedures for possible largest stroke are developed. Design charts are prepared for maximum stroke configuration. Stroke variation is an important concern in mechanism design. By adopting the introduced method, the output stroke can simply be adjusted even during the operation. The output stroke of the mechanism can be decreased more than 50% with proper transmission, velocity and acceleration characteristics. Use of non-integer gear ratio is also investigated. That property leads a variable stroke mechanism inherently. The relationship between the gear ratio and the number of cycles needed to return to the initial stroke value is determined. As a result, all possible design methods are investigated and generalized for this mechanism. Therefore, significant flexibility is introduced for adapting this mechanism to various practical applications.