# Solid mechanics

## Presentation

Programme (detailed contents):

Vector algebra. Axisymmetric vector fields. The “Torseur” formalism, or “screw”.

Types of forces. Vector representation of elementary forces. Moment about a point and about an axis, in 2-D & 3-D. Spatial force systems and equivalent “force torseur”, or “wrench”.

Linkages. Force transmissibility.

Statics, equilibrium of a rigid body.

Equilibrium of multibody systems. Analytical solutions. Static determinacy and indeterminacy. Graphical solutions in 2D.

Coulomb dry friction laws, friction angle. Grip and slip. 2D problems involving dry friction. Failover. Jamming.

Kinematics of particles: motion of a point, velocity, acceleration, trajectory.

Kinematics of a rigid body. “Kinematic Torseur” or “twist”: instantaneous rotation vector and velocity vector.

Absolute and relative motion. Kinematics of multibody systems.

General plane motion. Instantaneous rotation centre of a rigid body. Analytical and graphical solution of planar mechanisms.

Rotation about a fixed point. Euler's angles.

Dynamics of systems.

Examples with Matlab.

Organisation:

Lectures and tutorials and labs

## Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

-    Vector algebra fundamentals. The “Torseur” formalism.

-    The modeling of forces, the concept of moment of force.

-    The usual linkages between two rigid bodies; the modeling of the interaction forces.

-    The Statics fundamentals: principles for analysis of rigid body equilibrium, in 2-D & 3-D.

-    Kinematics fundamentals: principles for analysis of position, velocity, acceleration.

-    The relative motion; kinematics of rigid body systems.

-    Dynamics of systems

The student will be able to:

-    Set the force system modeling the action due to an external load or to a linkage on a rigid body.

-    Determine whether a rigid body, or a mechanism, is statically determinate or indeterminate.

-    Solve analytically the equilibrium of 3-D statically determinate problems.

-    Calculate the reactions at the supports and the interaction forces at the linkages.

-    Solve graphically problems involving 3 forces.

-    Solve analytically and graphically 2-D problems involving friction.

-    Calculate velocities and accelerations, absolute and relative.

-    Calculate various velocities of a rigid body particle, part of a mechanism.

-    Solve graphically kinematics problems related to planar mechanisms.

-    Solve Statics and Kinematics problems methodically and rigorously.

- Determine the mechanical loads and motions in dynamics systems

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...

## Additional information

Static, kinematics, dynamics of systems