In recent years, the potential for collision between humans and robots has drawn much attention since service robots are increasingly being used in the human environment. A safe robot arm can be achieved using either an active or passive compliance method. A passive compliance system composed of purely mechanical elements often provides faster and more reliable responses to dynamic collision than an active system involving sensors and actuators. Since positioning accuracy and collision safety of a robot arm are equally important, a robot arm should have very low stiffness when subjected to a collision force capable of causing human injury. Otherwise, it should maintain a very high stiffness. To implement these requirements, a novel safe joint mechanism (SJM-III) consisting of an inclined link, a slider with rollers, and linear springs is proposed. The SJM-III has the advantage of nonlinear stiffness, which can be achieved only with passive mechanical elements. Various analyses and experiments on static and dynamic collisions show high stiffness of the SJM-III against an external torque less than a predetermined threshold torque, with an abrupt drop in stiffness when the external torque exceeds this threshold. The safe joint mechanism enables a robot manipulator to guarantee positioning accuracy and collision safety, and which is simple to install between an actuator and a robot link without a significant change in the robot's design.