Soft continuum arms (SCAs) have a large workspace, dexterity, and adaptability, but at the cost of complex design construction highlighted by concatenating several serial segments. In this paper, we propose a new design architecture for SCAs composed of a parallel combination of pneumatic actuators. The BR2 SCA featured in this work is asymmetric as it combines one soft bending (B) actuator and two soft rotating (R2) actuators as opposed to state of art symmetric architectures that adopt bending segments. Spatial deformation is obtained by combining the bending and rotating feature of the individual actuators. This paper also formulates an approximate forward analysis method based on Kirchhoff rod equations to predict the spatial deformation under external loads with an accuracy less than 9% of the SCAs length. In addition, the model also takes into account the “coupling effect” inherent to the asymmetric parallel combination, where actuating rotating actuator attenuates the bending performance and vice versa. Consequently, this work also refines the design of the SCA that minimizes the coupling effect. A detailed performance study of the refined BR2 manipulator on a swiveling base demonstrates larger workspace and higher dexterity when compared with state of art single section SCAs. The performance of the design is validated through different tasks like obstacle avoidance, pick and place task, and whole arm grasping. These performance attributes surpass any other single segment soft module and is a potential building block for constructing customized SCAs.