04/19/04

     For this ideal calculation, we will neglect the weight of the lever arm, which would create a positive couple; we will also neglect the friction of the weight sliding on the pole, which would create a negative couple.

          ΣM_/shaft = T + 3.84 oz ∙ 36 in  –  16 oz  ∙ 12 in = 0

          T = 53.76 oz-in

     Since the servo is geared 1:2, we can expect the servo to apply a maximum of 92 oz-in, we only need about 60% of the servo's available output.

     Calculation of maximum theoretical lifting height:

     This is assuming that the servo will rotate the observed 110° of rotation, as well as a frictionless operation.

          Total lifting height:  H = h₁ + h₂

          H = 12" ∙ sin(27.5°) + 12" ∙ sin(27.5°)

          H = 11.1"

     Thus, the theoretical lift height is 11.1".  We only lifted 8.5", which is 77% of the theoretical value.

     Relation to maximum energy output of servo:

     The servo, in its original 1:1 gearing, has a maximum torque of 46 oz-in; so if the servo is attached to a disk of radius r (see image) which could just rotate about its axis, it would be operating at its maximum.

          ΣM_/C = T - 16 oz ∙ r

          r = 2.875"

     This system could raise the 16 oz weight a maximum of 7.02 in.

          Actual lift distance: 8.5"

          Counterweight actual vertical distance: 8.5" ∙ 36" ÷ 12" = 25.5"

     We were able to lift a higher distance than the theorized 7.02 inches because we are using the potential energy of a 3.84 oz counterweight and lowering it 25.5".  Thus,

          E_ours ÷ E_max = [16 oz ∙ 8.5" - 3.84 oz ∙ 25.5"] ÷ [16 oz ∙ 7.02"] = 33.9 %

     This means that we are only using approximately 34% of the maximum energy of the servo.

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Stress Analysis Project 2004 | The Mechanism | Performance | Features

This site was last updated 04/19/04