1. A method comprising; receiving three axes position and orientation requirements defining a tool control point (TCP) of a robotic manipulator, the robotic manipulator comprising at least seven revolute joints, wherein: the TCP is proximate to a distal end of the robotic manipulator, the distal end being proximate to a wrist joint, the wrist joint being articulable in a first set of three axes intersecting at a common wrist joint origin by way of a fifth revolute joint, a sixth revolute joint and a seventh revolute joint, the fifth axis of rotation being orthogonal to the sixth axis of rotation, and the seventh axis of rotation being orthogonal to the sixth axis of rotation; a shoulder joint is proximal to a proximal end of the robotic manipulator, the shoulder joint being rotatable about a first axis of rotation by way of a first revolute joint, about a second axis of rotation by way of a second revolute joint and about a third axis of rotation by a third revolute joint, the first axis of rotation being orthogonal to the second axis of rotation, and the third axis of rotation being orthogonal to the second axis of rotation; and the robotic manipulator further comprises an elbow joint disposed between the shoulder joint and the wrist joint, the elbow joint being rotatable about a fourth axis of rotation by way of a fourth revolute joint, the fourth axis of rotation being orthogonal to the third axis of rotation and to the respective axis of rotation of the fifth revolute joint; determining, with a controller, a set of solutions to an inverse kinematic relationship, the inverse kinematic relationship relating the received three axes position and orientation requirements defining the TCP to a respective angular position of each of the seven revolute joints, wherein the set of solutions specifies, in terms of an angular position of the first revolute joint and parameterized link lengths, at least one set of angular positions of the second, third, fourth, fifth, sixth and seventh revolute joints; and the set of solutions result from solving only closed-form mathematical expressions.