Update:Corected for dh_dl error 7/13/2012: dh_dl was 2, should have been .67 .
I wrote this excel program to calculate the height, speed, payload capability , current draw and lift time for a vertically linear actuated scissor lift. The inputs are the basic dimensions, number and type of motors, lift frame weight and manipulator weight plus design torque % of max torque.
I ran a test case based upon this posted Vex BLRS college robot in the Vex forum to see how it checked with the observed performance clarified in this post.
Excel Inputs based upon the post and picture.
The key inputs are the dh_dl which is the change in single stage height with actuactor extension. I initially noted that the linear slide actuators are attached to the mid-point lift pivot so a lift stage raises twice as much as the actuator and I chose dh_dl = 2. This however was incorrect . Although it is attached to a mid_point, this mid_point is on the second stage of the lift. Any motion of this point will only move the lower stage by 2/3 that amount. Therefore dh_dl should be equal to .67.
I also guessed at the W_manipulator = 6 lbs since it is not in the picture but the builder stated that it was heavy.
Also Friction is ignored since it is usually compensated for with elastic bands mounted horizontally between lift sides helping to propel the lift upwards.
The lift calculated extension time is 8.1 sec vs 7 to 8 sec noted by the robot builder. The total current (6. 4 amps) is reasonable… about 2 amps per power rail . The payload capability W seems very high (21 lbs) relative to just lifting 6 game objects. (3lbs). I don’t have a reasonable explanation other than the manipulator weighed much more than 6 lbs. If we argue that friction is not fully compensated for by rubber bands this would reduce the payload capability, however, it would also slow the lift time which is about right .
I will post this in the Vex forum and see whether test case holds up to scrutiny.
Perhaps later I will add a drag term to simulate uncompensated friction.
Excel calculated outputs;
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Performance Summary
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Calculated Values
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h_min_stage
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3.1
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in
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starting height per stage
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h_max_stage
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11.6
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in
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finishing height per stage
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h_min
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12.4
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in
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total starting height
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h_max
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46.4
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in
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total finishing height
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delta_h_stage
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8.5
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in
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Change in lift height per stage
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total_delta_h
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33.9
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in
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Total change in lift height
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torq_motor
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18.7
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in_lbs
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Available motor torque
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F_act
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74.8
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lbs
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Total actuator force pushing on frame
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I_total
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6.4
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amps
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Total current draw at speed
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W
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21.1
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lbs
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Total payload capability
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rpm_motor
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60.0
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rpm
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motor rpm during lifting
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t_lift
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8.1
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sec
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Lift extension time
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Program inputs:
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Scissor lift calculations
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Written by Vamfun 6/1/2012 Vamfun@yahoo.com Mentor 599 and 1508
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Vertical Linear slide actuating lift… 12 tooth gearing
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inputs
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percent_torq_stall
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40
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%
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Design torque in % of torq_stall
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W_manipulator
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6
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lbs
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Weight of manipulator
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W_f
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1.5
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lbs
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Weight of single stage of lift frame
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phi_min
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15
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deg
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Minimum angle between arm and horizontal
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phi_max
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75
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deg
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Maximum angle between arm and horizontal
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L_stage
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12
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in
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Total leg length per stage
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N
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4
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Number of lift stages
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r_gear
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0.25
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in
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gear radius used to convert motor motion to linear motion
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dh_dl
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0.67
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Change in single stage lift height per change in actuator extension
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torq_393
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14.76
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in_lbs
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Spec motor
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I_stall_393
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4.8
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amps
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Spec motor
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I_free_393
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0.37
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amps
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Spec motor
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n_393
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2
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User set number of motors
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torq_269
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8.6
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in_lbs
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Spec motor
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I_stall_269
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2.6
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amps
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Spec motor
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I_free_269
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0.18
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Spec motor
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n_269
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2
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User set number of motors
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