The appropriate design methodology is used to model uncertainties and variations in the design of a crank-rocker four-bar linkage. Each design parameter is modelled as a closed interval, such that the appropriate design of a linkage describes a family of linkages. Interval analysis routines are developed and applied to reliably determine the range of performance of the family of linkages. Appropriate synthesis concerns the determination of the complete set of appropriate design solutions which satisfy a given task. Here, a task is modelled with multiple precision points with allowable errors (i.e., boxes). An appropriate design solution must generate a coupler curve which passes within all precision points. Any linkage design contained within the set of appropriate design solutions is guaranteed to satisfy the task requirements.