This　study　presents　three　new　screw-based　inverse　kinematics　(IK)　sub-problems　and　their　corresponding　models,　which　could　be　applied　to　find　the　IK　solutions　for　manipulators　with　rotational　joints.　The　three　sub-problems　are　described　as:　rotation　about　three　axes　with　two　intersecting　axes　that　do　not　intersect　with　a　third　axis　or　three　non-intersecting　and　non-coplanar　axes;　rotation　about　four　axes　and　either　the　second　or　third　joint　angle　is　known;　and　rotation　about　five　axes　and　the　second　and　fourth　joint　angles　are　known.　In　the　IK　models,　the　rotational　motion　of　a　single　point　located　outside　of　the　axes　can　be　described　by　using　a　system　of　multivariate　quadratic　equations　based　on　the　geometrical　relationship.　According　to　these　descriptions,　each　sub-problem　is　converted　into　three　PK-1　sub-problems.　To　demonstrate　the　generality　of　the　sub-problems　to　different　manipulators,　the　IK　models　were　used　to　solve　the　IK　problems　for　the　robots　with　four,　six,　and　eight　degrees　of　freedom　(DOF)　respectively.　Moreover,　considering　the　4-DOF　robot　(a　redundant　manipulator)　as　the　research　object,　the　computational　efficiency　and　applicability　of　the　presented　IK　models　were　proven　by　applying　the　IK　solutions　to　a　robotic　trajectory　planning　problem　with　obstacle　avoidance　in　a　real　setting.　(C)　2018　Published　by　Elsevier　Inc.