A new line of very high precision actuators has been developed by the author (Hatheway, 1988). One of the features of these actuators is a very high degree of linearity over the full range of motion. The actuators are based upon an elastic transducer design which should make both the linear and nonlinear characteristics of the actuator predictable from the basic theory of elasticity. The author has measured the characteristics of a typical actuator based upon these elastic principles. In this report he shows that the nonlinearities are predictable from the elastic theory for large displacements. The actuators may be calibrated for 'open-loop' operation in applications requiring accuracies to 1.8 parts in 10,000 which is the limit of accuracy of this study.