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 midpoint 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;
Performance Summary


Calculated Values


h_min_stage

3.1

in

starting height per stage


h_max_stage

11.6

in

finishing height per stage


h_min

12.4

in

total starting height


h_max

46.4

in

total finishing height


delta_h_stage

8.5

in

Change in lift height per stage


total_delta_h

33.9

in

Total change in lift height


torq_motor

18.7

in_lbs

Available motor torque


F_act

74.8

lbs

Total actuator force pushing on frame


I_total

6.4

amps

Total current draw at speed


W

21.1

lbs

Total payload capability


rpm_motor

60.0

rpm

motor rpm during lifting


t_lift

8.1

sec

Lift extension time

Program inputs:
Scissor lift calculations


Written by Vamfun 6/1/2012 Vamfun@yahoo.com Mentor 599 and 1508


Vertical Linear slide actuating lift… 12 tooth gearing


inputs


percent_torq_stall

40

%

Design torque in % of torq_stall


W_manipulator

6

lbs

Weight of manipulator


W_f

1.5

lbs

Weight of single stage of lift frame


phi_min

15

deg

Minimum angle between arm and horizontal


phi_max

75

deg

Maximum angle between arm and horizontal


L_stage

12

in

Total leg length per stage


N

4

Number of lift stages


r_gear

0.25

in

gear radius used to convert motor motion to linear motion


dh_dl

0.67

Change in single stage lift height per change in actuator extension


torq_393

14.76

in_lbs

Spec motor


I_stall_393

4.8

amps

Spec motor


I_free_393

0.37

amps

Spec motor


n_393

2

User set number of motors


torq_269

8.6

in_lbs

Spec motor


I_stall_269

2.6

amps

Spec motor


I_free_269

0.18

Spec motor


n_269

2

User set number of motors
