Safe tool-tissue interaction is critical in medicine. The exerted force or torque on the tissue is required to be under control. This paper presents a design framework for producing simple mechanisms with adjustable constant force or torque. The constant load is generated by paralleling a positive constant stiffness spring and a negative constant stiffness mechanism. The combined output load can be tuned by simply changing the preload of the positive stiffness spring. Also, an algorithm is proposed as a key component of the design framework for assisting the design of the negative stiffness mechanism. By determining a prescribed stiffness that meets the requirement of the application, the proposed algorithm which consists of a finite element simulation (FES) and genetic algorithm (GA) seeks a proper beam structure through iterative optimization automatically. Two example applications are provided to demonstrate the effectiveness of using the design method in satisfying medical needs. Specifically, one translational application and one rotational application are used to show the capability and the versatility of the design framework. According to the experimental results of both examples, the produced mechanisms are able to output a required constant load along the target displacement consistently, and the output load magnitude can be controlled online.