Closed-form mechanisms of relative manipulation robot is an effective structure which helps to improve the accuracy and flexibility in technological processes. Unfortunately, the requirement about knowledge of exact dynamics of closed-form mechanisms of relative manipulation robot is arduous since it consists of numerous joints and links, and the identification of the kinematic relationship of closed-form structure is also complicated. This causes several shortcomings for controlling closed-form mechanisms of relative manipulation robot by using vector control algorithms because these methods require exactly dynamical equations of control systems. In contrast, the fuzzy controllers do not require knowledge of detailed mathematical equations of the control system since the fuzzy sets aim to capture the semantics of natural linguistic terms present in the fuzzy controller knowledge. Moreover, they have capability of handling uncertain and noisy signals, this helps to deal with the external environmental forces. This article proposes a fuzzy-based controller for closed-form mechanisms of relative manipulation robot to overcome mentioned problems by eliminating the identification of exact dynamics and kinematic constraints of closed-form structure. To verify the performance of the proposed method, the fuzzy-based controller is applied to a welding task by using a model of two-component mechanism which includes one closed-form manipulator and one serial manipulator. The welding task is also conducted by using conventional controllers in which the detailed dynamical equation is applied for the proportional-derivative (PD)-type and proportional integral derivative (PID)type computed torque controllers, whereas the fuzzy-based controller just uses several nominal parameters.