Vehicle　passing　angles　are　critical　metrics　for　evaluating　the　geometric　passability　of　vehicles.　The　accurate　measurement　of　these　angles　is　essential　for　route　planning　in　complex　terrain　and　in　guiding　the　production　of　specialized　vehicles.　However,　the　current　measurement　methods　cannot　meet　the　requirements　of　efficiency,　convenience　and　robustness.　This　paper　presents　a　novel　measurement　method　by　building　and　measuring　the　point　cloud　of　a　vehicle　chassis.　Based　on　this　method,　a　novel　measurement　system　is　designed　and　its　effectiveness　is　verified.　In　the　system,　a　wheeled　robot　acquires　and　processes　data　after　passing　underneath　the　vehicle.　Then,　we　introduce　a　new　approach　to　reduce　the　main　sources　of　error　when　building　point　clouds　beneath　the　vehicle,　achieved　by　modifying　the　extraction　algorithm　and　the　proportion　of　different　feature　points　in　each　frame.　Additionally,　we　present　a　fast　geometric　calculation　algorithm　for　calculating　the　passing　angles.　The　simulation　experiment　results　demonstrate　deviations　of　0.06252%,　0.01575%,　and　0.003987%　when　comparing　the　calculated　angles　to　those　of　the　simulated　vehicle.　The　experimental　results　show　that　the　method　and　system　are　effective　at　acquiring　the　point　cloud　of　the　vehicle　and　calculating　the　parameters　of　passing　angles　with　good　data　consistency,　exhibiting　variances　of　0.12407,　0.12407,　and　0.69804.