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Scissor Lift Design and Analysis Equations

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Scissor Lift Design and Analysis Equations
Mathematical Analysis of Scissor Lifts
H. M. Spackman

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Introduction

The purpose of this document is to present mathematical equations for analyzing reaction forces in scissor lifts and to discuss several design issues including actuator placement, and strength and rigidity. In section 2.0 the nomenclature is presented. In section 3.1 equations are derived for the scissor members whose reaction forces are not affected by the actuators. In section 3.2, equations for calculating the actuator forces directly are given. In section 4.0 the equations from sections 3.1 and 3.2 are combined into a single method of determining the reaction forces throughout the lift. Forces obtained from this analysis can be used in selecting the appropriate material and cross-section of the scissor members, and to select suitable actuators. In the remaining sections the design issues listed above are discussed.

TOC

1.0 Introduction ....................... ................................................ 1
2.0 Nomenclature ...................................................................... I
3.0 General Scissor Lift Equations .......................................... 4
3.1. Equations for the Basic Scissor Structure ....................................... 5
3.1.1 Load 1: Centered Load in the Negative y Direction .................. 5
3.1.2 Load 2: Moment About the z Axis ..................................... 9
3.1.3 Load 3: Centered Horizontal Load in the Positive x Direction ..... 12
3.1.4 Load 4: Centered Load in the Positive z Direction ................... 19
3.1.5 Load 5: Moment About the x Axis ..................................... 24
3.1.6 Load 6: Moment About the y Axis ..................................... 26
3.2. Equations for the Actuator ....................................... ............... 30
3.2.1 Derivation of dh/df Assuming Both Actuator Ends are Pinned to a Scissor Member ...................................................... 35
3.2.2 Derivation of dh/df Assuming One Actuator End is Pinned to Ground .................................................................. 39
4.0 CALCULATION OF REACTION FORCES ........................................ 45
5.0 ACTUATOR PLACEMENT ........................................................... 47
6.0 STRENGTH AND RIGIDITY ......................................................... 53
7.0 Conclusion .......................................................................... 56
8.0 Bibliography ........................................................................ 56

FIGURES
1. Nomenclature: applied loads and scissor lift dimensions ............................. 2
2. Nomenclature: reaction forces ........................................................ 3
3. Scissor lift models ....................................................................... 4
4. Basic scissor structure with load applied in the negative y direction ................ 7
5. Free body diagrams for load applied in the negative y direction .................. 7
6. Basic scissor structure with a moment about the z axis .............................. 0
7. Free body diagrams for applied moment about the z axis .......................... 10
8. Basic scissor structure with load applied in the positive x direction ................ 13
9. Free body diagrams for load applied in x direction with the back joints pinned ......................................... .. .......... . 13
10. Free body diagrams for load applied in x direction with the front joints pinned .......................... . . ............................ 17

II. Basic scissor structure with load applied in the positive z direction ................ 20
12. Deflections and reaction forces for load applied in the positive z direction ....... 20
13. Free body diagrams for load applied in the positive z direction .................... 22
14. Basic scissor structure with applied moment about the x axis ....................... 25
15. Free body diagrams for an applied moment about the x axis ........................ 25
16. Basic scissor structure with applied moment about the y axis ...................... 27
17. Free body diagrams for an applied moment about the y axis ........................ 27
18. Four level lift loaded in the x and y directions ....................................... 31
19. U n ifo rm m ass .............................................................................. 3 1
20. n-level lift with actuators attached between the bottom joints ....................... 33
21. Coordinates of a point on the lift ....................................................... 35
22. Path traveled by a point on a positively sloping scissor member .................... 36
23. Length of an actuator attached between two points on a lift ........................ 38
24. Actuator position and displacement nomenclature ................................... 40
25. Actuator models ........................................................................... 43
26. Detailed n-level scissor lift .............................................................. 46
27. Possible actuator locations ............................................................... 47
29. Weightless n-level lift with actuator between left joints of level i ................... 49
30. Normal and tangential forces ............................................... ........... 52
31. Summary of reaction forces ... ........................................ ................. 54
32 . Crossbracing ............................................................................... 55

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