Inverse　kinematics　(IK)　is　a　significant　theoretical　foundation　for　the　real　application　of　redundant　manipulators.　In　existing　methods,　the　Denavit-Hartenberg　(DH)　conversion　and　screw-based　IK　sub-problems　have　been　utilized　to　calculate　the　inverse　solution,　but　would　be　limited　by　some　special　manipulators’　configurations　or　cannot　obtain　exact　solutions.　In　this　paper,　an　exact　inverse　solution　for　a　7R　manipulator　is　modeled　based　on　screw　theory.　In　the　modeling,　firstly　assuming　that　the　first　joint　is　known,　the　total　motion　of　all　joints　are　divided　into　three　steps　of　operational　motions:　Rotation　about　the　second,　third　and　fourth　joints;　Rotation　about　the　five　and　six　joints;　And　rotation　about　the　last　joint.　Problems　for　the　first　two　rotations　can　be　both　modeled　based　on　a　novel　screw-based　sub-problem.　Finally,　the　angular　displacements　of　six　joints　are　formulated　explicitly　in　terms　of　the　redundant　joint　angle.　Using　the　proposed　method,　all　exact　solutions　can　be　obtained　by　traversing　values　of　the　redundant　angle.　The　effectiveness　and　efficiency　of　the　proposed　technique　is　validated　using　a　simulation　in　MATLAB.　©　2023,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.