Grasping and twisting motions are vital when manipulating objects due to their fundamental role in enabling precision, adaptability, and effective interaction. However, few studies in soft robotics exploiting artificial muscles have achieved object manipulation in situ through the coordination of twisting and grasping motions akin to our forearm and hand's capabilities. Especially, when using the same artificial muscle module to achieve these two motions will greatly simplify the manufacturing and control complexity. Here, we introduce identical origami artificial muscle modules (OAMMs) subjected to distinct end constraints into the design of the robotic manipulator, allowing it to achieve independent grasping and twisting motions to achieve effective, precise object manipulation. Applying different end constraints to the identical OAMMs yields distinct motions at their ends, where utilizing a fixed end and a sliding end realizes pure translation, while opting for a fixed end and a rotating end enables pure rotation. The differentially constrained OAMMs then serve as soft actuators for the manipulator's torsional mechanism and grasping mechanism to accomplish independent, controllable twisting and grasping motions. The coordination of twisting and grasping motions finally enables the manipulator to complete various tasks, including installing a light bubble, pouring the water from a lidded bottle into a cup, and sorting and stacking puzzle blocks. Our study pioneers the utilization of OAMMs for precise and versatile object manipulation through the coordination of independent twisting and grasping motions.