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ICs and Mechanical Advantage (MA) Lecture 8 Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Mechanical Advantage (MA) ¾ The Mechanism is a conservative system ¾ Inertial and friction effects are ignored for the system Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Examples Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Mechanical Advantage ¾ Definition: Ratio of force-out over force-in ¾ Force, Velocity, and Torque are typically constant for a linkage Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Mechanical Advantage Tin =Findin =Foutdout =Tout Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Mechanical Advantage ¾ M.A. is a product of two factors ¾ Ratio of distances that depend n the placement of the input and output forces ¾ An angular velocity ratio ¾ Can be expressed entirely in terms of direct distances ¾ Based on the instant center development Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Mechanical Advantage ¾ If we know the angular velocity ratio between the input and the output link, M.A. can be expressed entirely in terms of ratios of distances Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT M.A. and Instant Center An angular velocity ratio can be expressed entirely in terms of direct distances Based on the instant center development Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT M.A. and Instant Center din ωin ⋅ M . A. = d out ωout V din rin = ⋅ d out V rout din rout = ⋅ d out rin Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Drive Mechanism Example ¾ Handle is being pulled to left with force Fin ¾ Pressure difference across the piston in the cylinder is resisting the movement by a force equal and opposite to Fout din dout Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Solution dout Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Toggle Position Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Example #2 Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT MA for a Slider Crank MA needs to be modified Link 4 Constrained to move in the horizontal direction Fout is constrained to be in the horizontal direction rin din Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT MA Slider Crank ( Power )in = ( Power )out r v r r r T2 o ω2 = Fout o vB where vB = rin ⋅ ω2 din ⋅ Fin ⋅ ω2 = rin ⋅ Fout ⋅ ω2 MA = Fout din = Fin rin rin din Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Six Bar Linkage Determine the MA of this system Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Instant Centers for 6 Bar Linkage Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT Can Crusher Example Union College Mechanical Engineering MER 312: Dynamics and Kinematics (of Mechanisms) / AT
