Kinematic and Geometric Analysis of a Mobile-Fulcrum Lever with Torque-Displacement Decoupling

This paper introduces the Mobile-Fulcrum Lever (MFL), a new class of planar lever mechanisms characterized by a fulcrum that is fixed in a rotating reference frame while undergoing prescribed orbital motion in the inertial frame due to a dual-frame kinematic constraint. The resulting architecture forms a single-degreeof-freedom closed kinematic chain whose internal geometry evolves with the rotation of the mobile frame, giving rise to motion and force transmission characteristics not attainable in classical levers or slider-crank mechanisms. A complete geometric and analytical formulation of the MFL is developed, including the mapping between inertial and rotating reference frames, the loop-closure conditions governing the floating joint, the strokeangle Jacobian associated with linear actuation, and the evolving moment-arm structure responsible for torque transmission. The analysis yields three principal theoretical results. First, the MFL exhibits exceptionally low average stroke-angle Jacobians over a wide operating range, enabling large angular displacements from limited linear strokes and yielding angular amplification factors on the order of magnitude relative to slider-crank mechanisms under equivalent geometric constraints. Second, the orbital motion of the fulcrum combined with constraint-induced internal lever rotation maintains the effective torque arm nearly orthogonal to the applied force over an extended angular interval, resulting in an approximately constant torque and the avoidance of classical dead-center singularities. Third, torque transmission and angular displacement are shown to be governed by distinct geometric vectors that evolve independently, establishing a fundamental decoupling between torque and rotation that does not exist in conventional lever and crank-based systems. The analytical framework presented here generalizes experimentally observed behavior of mobile-fulcrum lever mechanisms and provides a foundation for the systematic synthesis and analysis of a broader family of dual-frame motion conversion mechanisms, with potential relevance to rotary actuation and energy conversion applications.