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Proteins achieve their complex functions, such as molecular recognition with high affinity and specificity, through intricate three-dimensional geometries in functional sites. To engineer new protein functions, accurate positioning of amino acid functional groups is therefore critical but has remained difficult to achieve by computational methods because of current limitations in the design of new conformations with arbitrary user-defined geometries. Here, we introduce two computational methods capable of generating and predicting new local protein geometries: fragment kinematic closure (FKIC) and loophash kinematic closure (LHKIC). FKIC and LHKIC integrate two approaches: robotics-inspired kinematics of protein conformations and insertion of peptide fragments. We show that FKIC and LHKIC predict native-like conformations at atomic accuracy and with up to 140-fold improvements in sampling efficiency over previous approaches. We then use these methods to create a design protocol, pull into place (PIP), to position functionally important side chains via design of backbone conformations. We validate PIP by remodeling a sizeable active site region in an enzyme and confirming the engineered new conformations of two designs with crystal structures. The described methods can be applied broadly to the design of user-defined geometries for new protein functions.