The first step for combining supports is to compare the coordinate systems in which the supports are defined. This comparison lets you determine if the axes of the systems coincide, that is, if any of the axes of the system of the second support corresponds (is parallel) to a selected axis of the first support system. In the 3D Cartesian coordinate system, the following cases are possible:
- Three axes coincide
- One axis coincides with another
- The axes do not coincide.
For coinciding axes of the support coordinate systems, the support methods are composed (summed) according to the following rules:
- If a direction is fixed for any support, this direction is also fixed for the resulting support.
- If a direction is entirely released for any support, then for the resulting support, the support method for this direction is copied from the other support.
- The rigidity and damping coefficients for the resulting support are a sum of the corresponding coefficients for the component supports.
- Characteristics of non-linear supports cannot be summed, except for Rules 1 and 2.
- Unilateral supports can completely block a given degree of freedom. For example, one of the supports blocks motion in the direction +; whereas, the other one blocks in the direction -.
If the axes of the support coordinate systems do not coincide, a projection must be performed for the following situations:
- 3D projection - When none of the support axes coincides with the axis of the other support.
- 2D projection - When one of the support axes coincides with the axis of the other support, while the remaining two axes are inclined towards each other.
For 3D projections, the analysis is run as follows:
- For each support, a vector of fixed directions is defined (separately for displacement degrees of freedom and separately for rotational degrees of freedom)
- Mutual relations of fixed direction vectors are analyzed. The purpose of the first check is to eliminate the situation that all 3 directions are fixed (vectors form a non-coplanar 3D system). After the analysis is completed, then it might be possible that motion is not blocked for 1 or 2 directions.
- On this direction (directions), rigidity and damping vectors for both component supports are projected.
- If non-perpendicular vectors of released directions of rotation and displacement are obtained, after analyzing the fixed degrees of freedom for displacements and rotations, the resulting support is incorrect.
- Unilateral and non-linear supports cannot be projected.
For 2D projections, the algorithm is similar to 3D projections. The basic difference is that all operations are performed within a plane: there are 2 degrees of freedom.
Remember, for the resulting support, a local coordinate system is defined that does not have to coincide with the systems of the component supports. Names of the directions from the component supports (XYZ) do not need to coincide with directions in the resulting support.