Shape Memory Alloy (SMA) based actuators have been commonly used in applications that require being compact and lightweight. In this paper, the inherent stiffness of a flexure-based linear guide is used to create a bias-spring SMA actuator which further reduces the work weight density of such a class of actuator. Using a flexure-based magnetic latch system, the SMA actuator behaves as a mechanical oscillator that requires no electronics or control strategy. A thermal model is presented and validated such that the mechanical oscillator can be easily sized for the required application. A working prototype, measuring 60 mm x 50 mm x 10 mm in dimension weighing 10.2 g, is showcased in this work. This concept would be ideal for bio-mimetic mobile robots such as inchworm robots.