The mobility is analyzed for the 4R1P-type planar closed-loop five-bar linkages using characteristics charts and four-bar Grashof criterion by introducing the virtual link. Based on dimensional relations of the three RR-type links, the five-bars are divided into three categories: Class I, Class II and Class III. Class I satisfies rmax < rmid + rmin, Class II satisfies rmax > rmid + rmin and Class III holds the equality. In the characteristics charts, Class I has a circular slide reachable range with two Grashof regions and two non-Grashof ones separated by three Grashof boundaries C1, C2 and C3, as well as one structure boundary B3; Class II has a ringed range with one Grashof region and two non-Grashof ones separated by the void boundary A1 instead of C1, two Grashof boundaries C2 and C3, as well as B3; and Class III has a circular range with three regions separated by C2, C3 and B3. From the four-bar Grashof criterion, the five-bars have two fully revolute joints at the Grashof regions while no such joints at the non-Grashof regions. Specially, the five-bars have Grashof change points at the Grashof boundaries and keep in line at A1 and B3. Each class includes further sub-classes. Several cases are illustrated for the applications.

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