解：?$(1)$?∵?$C$?是線段?$AB$?的中點(diǎn)，?$AB=8\ \mathrm {cm}$?
∴?$BC=\frac {1}{2}AB=4(\mathrm {cm})$?
∴?$CD=BC-BD=4-3=1(\mathrm {cm})$?
?$(2)①$?當(dāng)點(diǎn)?$E$?在點(diǎn)?$B$?的右側(cè)時(shí)，如圖
∵?$BE=\frac {1}{3}BD$?，?$BD=3\ \mathrm {cm}$?，∴?$BE=1\ \mathrm {cm}$?
∵?$F $?是線段?$BE$?的中點(diǎn)，∴?$BF=\frac {1}{2}BE=\frac {1}{2}(\mathrm {cm})$?
∴?$CF=BC+BF=4\frac {1}{2}(\mathrm {cm})$?
?$②$?當(dāng)點(diǎn)?$E$?在點(diǎn)?$B$?的左側(cè)時(shí)，如圖
∵?$BE=\frac {1}{3}BD$?，?$BD=3\ \mathrm {cm}$?，∴?$BE=1\ \mathrm {cm}$?
∵?$F $?是線段?$BE$?的中點(diǎn)
∴?$BF=\frac {1}{2}BE=\frac {1}{2}(\mathrm {cm})$?
∴?$CF=BC-BF=3\frac {1}{2}(\mathrm {cm})$?
綜上，線段?$CF $?的長(zhǎng)為?$4\frac {1}{2}\mathrm {cm} $?或?$3\frac {1}{2}\mathrm {cm}$?
