# Linear Actuator Force Calculations

Equations of motion are described herein to determine the axial and radial loads applied to the carriage assembly when subjected to typical load scenarios, which can then be utilized to determine “Load/Life” characteristics.

 a = acceleration, [m/s2] c = Carriage d = Horizontal distance of payload center of gravity from carriage center, [m] F = Force applied by belt (belt working load) or chain (avg. tensile strength), [N] FAx = Axial / Thrust Load Capacity of Dual Vee Wheel, [N] FFr = Frictional force, [N] =μg(Mc+ Mp) FRa = Radial Load Capacity of Dual Vee Wheel, [N] g = Gravitational Acceleration = 9.81 m/s2 h = Vertical distance of payload center of gravity from carriage center. [m] Mp = Payload Mass, [kg] n = Carriage Wheel Track (distance between track vees), [m] p = Payload RAx = Wheel Axial Reaction Force, [N] RRa = Wheel Radial Reaction Force, [N] μ = Coefficient of Friction, [N/N] = .015 Wp = Payload Weight, [N] WALC = Wheel Axial Load Capacity WRLC = Wheel Radial Load Capacity x = Carriage Wheel Base, [m] TP = Torque applied to carriage induced by payload.

Load Scenario 1 Load Scenario 2 Load Scenario 3 Load Scenario 4 Load Scenario 5 Load Scenario 6 Load Scenario 7 Load Scenario 8 