A spatial parallel-architecture robotic Carpal wrist is shown. The structure of the robotic Carpal wrist allows for the application of a closed-form solution to the kinematic problem of determining all of the possible inputs to the actuators that result in a desired end orientation of the distal plate. The robotic Carpal wrist has a structure including a base plate, a distal plate and six equal length links connecting the base plate to the distal plate with the six links being arranged in three chains of two links each and with three actuators being mounted in fixed relationship to the base plate. The three actuators cause the three links connected to the base plate to each pivot with a single degree-of-freedom relative to the base plate. Each of the three chains of links includes a three degree-of-freedom joint between its two links. The distal plate is connected to three of the links with the connection between the distal plate and each of the three links allowing a single degree-of-freedom between the distal plate and each of the three links.