As an important branch of reconfigurable robots, extensible continuum robots are soft and light, with the flexibility of movement and high adaptability in complex environments. These robots have very broad applications in a variety of fields, including military reconnaissance, geological exploration and rescue operations. In this paper, a high folding ratio, flexible, and compact extensible continuum arm is designed using a novel combination of parallel and deployable mechanisms. We present the spherical-linkage parallel mechanism (SLPM) as a flexure hinge. The analysis suggests that the SLPM is highly flexible and meets the requirements for many DoFs (degrees-of-freedom) needed in various fields. The folding ratio of the SLPM was 72.73. Following this, we present an SLPM compliant module powered by a set of embedded shape memory alloy (SMA) springs. These can change the internal elasticity of the module as temperature changes, thereby varying the stiffness. Moreover, the control system is designed to enable real-time cooperation between multiple motors and carries out simulations for deployable motion. The extensible continuum arm prototype was manufactured and its performance was tested in complex environments. From the results, it is shown that the arm can be utilized for rescue during disasters as well as investigation and repair of aircraft engines.