Kinematic determinacy
Encyclopedia
Kinematic determinacy is a term used in structural mechanics
to describe a structure where material compatibility conditions alone can be used to calculate deflections.
A kinematically determinate structure can be defined as a structure where, if it is possible to find nodal displacements compatible with member extensions, those nodal displacements are unique. The structure has no possible mechanisms, i.e. nodal displacements, compatible with zero member extensions, at least to a first-order approximation. Mathematically, the mass matrix
of the structure must have full rank.
Kinematic determinacy can be loosely used to classify an arrangement of structural members as a structure (stable) instead of a mechanism (unstable).
The principles of kinematic determinacy are used to design precision devices such as mirror mount
s for optics, and precision linear motion bearing
s.
Structural mechanics
Structural mechanics or Mechanics of structures is the computation of deformations, deflections, and internal forces or stresses within structures, either for design or for performance evaluation of existing structures. It is one subset of structural analysis...
to describe a structure where material compatibility conditions alone can be used to calculate deflections.
A kinematically determinate structure can be defined as a structure where, if it is possible to find nodal displacements compatible with member extensions, those nodal displacements are unique. The structure has no possible mechanisms, i.e. nodal displacements, compatible with zero member extensions, at least to a first-order approximation. Mathematically, the mass matrix
Mass matrix
In computational mechanics, a mass matrix is a generalization of the concept of mass to generalized coordinates. For example, consider a two-body particle system in one dimension...
of the structure must have full rank.
Kinematic determinacy can be loosely used to classify an arrangement of structural members as a structure (stable) instead of a mechanism (unstable).
The principles of kinematic determinacy are used to design precision devices such as mirror mount
Mirror mount
A mirror mount is a device that holds a mirror. In optics research, these can be quite sophisticated devices, due to the need to be able to tip and tilt the mirror by controlled amounts, while still holding it in a precise position when it is not being adjusted.Precision mirror mounts can be quite...
s for optics, and precision linear motion bearing
Linear motion bearing
A linear-motion bearing or linear slide is a bearing designed to provide free motion in one dimension. There are many different types of linear motion bearings and this family of products is generally broken down into two sub-categories: rolling-element and plane.Motorized linear slides such as...
s.
See also
- Statical determinacyStatical determinacyStatical determinacy is a term used in structural mechanics to describe a structure where force and moment equilibrium conditions alone can be utilized to calculate internal member actions....
- Precision engineeringPrecision engineeringPrecision engineering is a subdiscipline of electrical engineering, electronics engineering, mechanical engineering, and optical engineering concerned with designing machines, fixtures, and other structures that have exceptionally low tolerances, are repeatable, and are stable over time...
- Kinematic couplingKinematic couplingKinematic coupling describes fixtures designed to exactly kinematically constrain the part in question. A canonical example of a kinematic coupling consists of three radial v-groves in one part that mate with three hemispheres in another, credited to Maxwell...