Position　control　of　nonholonomic　3R　underactuated　robots　is　investigated　in　this　paper.　A　new　method　is　proposed　for　motion　control　of　this　kind　of　system.　The　control　objective　is　to　move　the　links　from　rest　to　target　configuration　with　zero　velocity.　The　whole　control　process　can　be　divided　into　two　stages,　the　first　stage　is　to　achieve　the　position　control　of　first　link　based　on　the　dynamic　model,　the　desired　position　of　the　second　active　and　third　passive　links　are　reached　in　the　second　stage　without　considering　the　motion　of　first　link.　Fuzzy　control　method　is　introduced　in　the　second　stage　and　the　motion　of　the　system　can　be　considered　to　be　the　resultant　motion　of　the　folding　or　unfolding　of　passive　joints　and　the　revolution　of　active　joints.　The　genetic　algorithm　is　utilized　in　the　best　fuzzy　rules　generating.　At　last　numerical　simulations　illuminate　the　effectiveness　of　the　proposed　method.