The well-established methodology for slider-crank function generation states that five precision points can be achieved without structural error. The resulting designs, however, do not necessarily satisfy all of the kinematic requirements for designing a slider-crank linkage used in common machine applications such as driving the ram of a mechanical press. First, linkage solutions to the five precision point synthesis problem may need to change circuits to reach the precision points. Second, there is no guarantee that the input crank is fully rotatable. This paper presents a modification to the function generation synthesis methodology that reveals a continuum of defect-free, slider-crank solutions for four precision points. Additionally, the methodology allows the specification of velocity or acceleration at the precision points. Although smaller accelerations at a point of zero slide velocity are associated with longer dwell, a point having zero velocity and acceleration is shown not to be possible. Examples are included to illustrate this kinematic synthesis methodology.