This paper presents a new systematic method for dealing with overconstrained mechanisms, and describes how the method was used to discover new overconstrained mechanisms and correct errors in several previously published overconstraint conditions. With this one method we are able to verify all previously known overconstrained mechanisms. In addition, this method yields the input-output equations of any single-loop overconstrained mechanism. For all new and corrected overconstrained mechanisms, numerical examples of input-output curves are presented.