concept of force

The concept of particle and rigid body

concept of balance

Principle of two-force balance: two forces of equal magnitude and opposite directions acting on the same straight line

The principle of adding and subtracting balanced force systems: Adding or subtracting any balanced force system to any force system acting on a rigid body does not change the effect of the original force system on the rigid body.

Parallelogram Law of Forces

Action and reaction theorem: A pair of forces interacting between two objects always exist at the same time and are equal in magnitude and opposite in direction. The lines of action are the same and act on the two objects respectively.

Rigidization principle: A deformable body is in equilibrium under the action of a certain force system. If the deformable body is rigidified into a rigid body, its equilibrium state remains unchanged.

Constraints: Limit movement and movement trends. Constraint forces: Forces that constrain the displacement of an object in a certain direction.

Flexible rope constraints: Steel wire ropes, belts, chains, nylon ropes, etc. in engineering can all be simplified into soft ropes

Constraints with smooth contact surfaces

Smooth cylindrical hinge constraints

Smooth ball hinge constraint

chain link constraint

Force diagram

Force analysis

Geometric method, analytical method can be calculated

Plane intersection force system: a force system in which the lines of action of each force intersect at a point

Plane parallel force system: a force system whose lines of action are parallel to each other

Plane arbitrary force system: a force whose lines of action are neither parallel nor intersecting at a point

The concept and equivalence of couples of forces

Synthesis and equilibrium of plane force couple system

Translation theorem of force: The force acting on a rigid body can translate to any point. After translation, a force couple is attached. The couple moment of the additional force couple is equal to the moment of the original force on the translation point.

Simplification of plane general force system to one point and principal vectors and principal moments

Equilibrium equations of plane general force system

Equilibrium equation of plane parallel force system

Static determination and overdetermination problems

Balance problem of rigid body system

Nodal method and section method can be calculated

Truss: A geometrically constant structure consisting of a number of straight rods connected by hinges at both ends.

Plane truss: All truss members are in one plane

Node: The connection between the members in the truss

Static sliding friction: objects only have a tendency to slide relative to each other, and the friction they experience

Maximum static friction: the maximum value reached by friction when an object is in critical equilibrium.

Dynamic sliding friction: When relative sliding occurs between contact surfaces, friction occurs between the contact surfaces that hinders the sliding of objects.

Friction angle: the maximum value of the angle between the full binding force and the normal line

Self-locking phenomenon: The resultant force of all active forces acting on the object is Fe. If the line of action is within the friction angle, the object will remain stationary no matter how large it is.