A rapidly mounted, modular, universal handrail and grab bar system uses mounting assemblies therefore. Each mounting assembly includes a clamp having through rail member recesses receiving a rail member generally perpendicular to a clamp longitudinal axis. The clamp includes a closed distal end and proximally extending clamp sides moving toward and away from each other effectively opening and closing the opening size to selectively clamp onto the rail member. A saddle has a curved distal end receiving the rail member, and opposed planar faces receiving the clamp sides, wherein the saddle includes a central fastener opening that extends generally along the saddle longitudinal axis and generally perpendicular to the rail member; and a flange coupled the saddle and fitting over the clamp and selectively moving the clamp sides toward each other to tighten the clamp onto the rail member by decreasing size of the opening.