Static CG configuration screen

Planar gravity moment

Inputs

Declared moving massmUser-entered mass acting at the stated center of gravity.

Pivot-to-CG radiusrUser-entered pivot-to-center-of-gravity radius.

Configuration angle from verticalθUser-entered planar angle between the gravity line and the pivot-to-CG radius; 0° produces no gravity moment.

Declared counter momentMcUser-entered static counteracting moment at the same pivot and sign convention.

Weight forceW

98.1

Gravity perpendicular lever arm

0.15

Signed gravity moment

14.715

Counter moment minus gravity moment

5.285

W = mg; r⊥ = r sin θ; Mg = mgr sin θ; Mresidual = Mc − Mg

A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.

Calculation snapshot

Formula version 1.0.0

Declared moving mass	10
Pivot-to-CG radius	0.3
Configuration angle from vertical	30
Declared counter moment	20

Weight force	98.1 N
Gravity perpendicular lever arm	0.15 m
Signed gravity moment	14.715 N·m
Counter moment minus gravity moment	5.285 N·m

W = mg · r⊥ = r sin θ · Mg = mgr sin θ · Mresidual = Mc − Mg

OpenStax torque reference: https://openstax.org/books/university-physics-volume-1/pages/10-6-torque

This printout is a record of displayed inputs and deterministic formula output. It is not an approval, certification, or engineering conclusion.

Method

Calculate a mass’s static gravity moment about one pivot and compare it with one entered counteracting moment at the same configuration.

W = mg; r⊥ = r sin θ; Mg = mgr sin θ; Mresidual = Mc − Mg

When

Don’t

This is a static single-point-mass, planar gravity-moment screen. It does not solve an over-center, toggle, or four-bar linkage; calculate actuator force/travel, joint reactions, locking, force amplification, self-locking, spring forces, friction, contact, dynamic/inertial loads, deflection, collision, stability, guard requirements, safety, or certification. Enter moments using a declared common sign convention and validate the real mechanism independently.