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This paper reports the rationale and design of a robotic arm, as inspired by an octopus arm. The octopus arm shows peculiar features, such as the ability to bend in all directions, to produce fast elongations, and to vary its stiffness. The octopus achieves these unique motor skills, thanks to its peculiar muscular structure, named muscular hydrostat. Different muscles arranged on orthogonal planes generate an antagonistic action on each other in the muscular hydrostat, which does not change its volume during muscle contractions, and allow bending and elongation of the arm and stiffness variation. By drawing inspiration from natural skills of octopus, and by analysing the geometry and mechanics of the muscular structure of its arm, we propose the design of a robot arm consisting of an artificial muscular hydrostat structure, which is completely soft and compliant, but also able to stiffen. In this paper, we discuss the design criteria of the robotic arm and how this design and the special arrangement of its muscular structure may bring the building of a robotic arm into being, by showing the results obtained by mathematical models and prototypical mock-ups.