---
title: "Scissor Lift & Virtual Work Interactive Lab | Sandbox Physics"
description: "Why is a scissor lift hardest to raise near the ground? With the bars nearly flat, a small inward pull at the bottom slider raises the weight a large distance. The horizontal drive must supply more force to provide that increase in gravitational energy. As the bars stand up, the same inward travel lifts the platform less, so the force needed for slow lifting falls."
canonical_url: "https://sandboxphysics.com/labs/scissor-lift/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/scissor-lift/"
last_modified: "2026-10-23"
---

Mechanisms · Slow lifting

# Scissor Lift & Virtual Work

**Why is a scissor lift hardest to raise near the ground?** With the bars nearly flat, a small inward pull at the bottom slider raises the weight a large distance. The horizontal drive must supply more force to provide that increase in gravitational energy. As the bars stand up, the same inward travel lifts the platform less, so the force needed for slow lifting falls.

Pull a horizontal slider inward and watch two crossed bars raise a level platform. Change the weight and arm length, compare the required drive force, and follow how input work becomes gravitational potential energy.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

One ideal scissor stage is driven at its bottom sliding pin. The load acts vertically on the level platform. Force values assume slow, static lifting with massless links and frictionless joints. Playback is a geometry sweep; inertia, friction, buckling, tipping and actuator losses are omitted.

Physics tutorial

## Why the lift needs more force near the bottom

**Background** A horizontal pull can raise a platform through two crossed bars. The same pull moves the platform very differently at different heights.

**Why it matters** The hardest part of a lift is often the first few centimetres. The motion ratio explains why.

Start with the essentials

- **Focus question**: Why does the horizontal drive need more force when the bars lie nearly flat?
- **One-sentence intuition**: Near the bottom, a short inward movement raises the weight a long way, so the drive must supply a larger force to provide the same work.

### Core mathematical model

#### Height and base spacing

$$
h=L\sin\theta,\qquad w=L\cos\theta
$$

The two crossed bars have the same pin-to-pin length. Their midpoint pin and equal lengths keep the upper pins at the same height.

#### Force from virtual work

$$
\mathrm ds=-\mathrm dw,\quad F\,\mathrm ds=W\,\mathrm dh,\quad F=W\cot\theta
$$

Inward travel is positive. Input work balances the rise in gravitational energy for massless links and a slowly lifted weight.

#### Work over the interval

$$
\int_0^s F(s')\,\mathrm ds'=WL(\sin\theta-\sin\theta_0)
$$

The graph integrates the left side numerically and compares it with the independent height expression on the right. The lowest allowed angle sets the zero of work.

### Common difficulties

#### The actuator location matters

**Typical misconception** Every scissor lift needs this same force at the same height.

**Better mental model** This force applies to one ideal stage pulled horizontally at its bottom slider. Moving a cylinder to a different pair of attachment points changes its stroke and force.

#### Static force is different from fast-motion force

**Typical misconception** A faster animation should need the same force in a real lift.

**Better mental model** The displayed force assumes slow lifting. A real rapid lift also needs forces for acceleration, friction and the moving structure's own weight.

### Run the experiment

1. 01

   #### Start near the ground

   Choose Near the ground and slowly drag the blue bottom slider inward.

   **What to observe:** The platform rises quickly for little inward travel. The required horizontal force is several times the supported weight.

2. 02

   #### Raise the bars

   Compare Force equals weight and Tall lift at the same weight.

   **What to observe:** The height gain per inward travel and the force ratio fall together. At a forty-five-degree arm angle, drive force equals the weight.

3. 03

   #### Compare work

   Choose Heavy load, then inspect the input-work and potential-energy curves. Change the sweep rate.

   **What to observe:** The two work curves nearly coincide. Faster playback changes how quickly you see the sweep, not the static force or work at a given angle.

Physical conclusion

A large motion gain costs force; slow ideal lifting exchanges equal input work and gravitational energy.

Sources: [US Army Engineer School · Engineering Drawing II, §6](https://files.eric.ed.gov/fulltext/ED221758.pdf) · [He et al. · Scissor lift virtual work](https://ietresearch.onlinelibrary.wiley.com/doi/full/10.1049/joe.2018.8961) · [MIT · Mechanical advantage](https://ocw.mit.edu/courses/2-007-design-and-manufacturing-i-spring-2009/29b95c6d8570f9aeb140c151747c96e3_MIT2_007s09_lec01.pdf)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)