Symmetric pre-dead-centre screen
Toggle linkage force
Inputs
Input force declared perpendicular to the symmetric toggle link line at the knee.
Positive pre-dead-centre angle of each link from the straight-line toggle position. The screen guards 0.5° and below.
Results
Ideal symmetric toggle mechanical advantage
5.715
—Ideal axial toggle output force
2,000.3
Declared-angle tangent
0.087489
—MA = 1/[2 tan(θ)] · Fout = Fin · MA
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Trapezoidal motion · Reflected inertia · Pneumatic cylinder force · Clamp-force transfer
Method
Formula, when it applies, and when it does not
Calculate ideal mechanical advantage and axial output force for a symmetric, planar, two-link toggle from a knee input and pre-dead-centre angle.
MA = 1/[2 tan(θ)] · Fout = Fin · MA
When
- Symmetric planar two-link geometry
- Knee input perpendicular to link line
- Ideal frictionless pins
- Positive pre-dead-centre angle only
Don’t
- This is an ideal, symmetric, planar, pre-dead-centre two-link toggle relation with a knee input perpendicular to the link line. It excludes link length and kinematics, frame/guide deflection, pin stress and clearance, friction, compliance, off-axis loading, stroke, actuation, over-centre travel, locking/self-locking, latch retention, material strength, fatigue, safety, and approval. It deliberately rejects the near-singular 0.5° and below range.
Shigley's Mechanical Engineering Design — linkage force transmission