Free mechanical set: defining the position
Position of the free mechanical set
The free motion is defined by a list of positions of the mobile mechanical set.
To define these positions, the mobile mechanical set will be dependent on the reference coordinate system.
Definition
Let us consider:
- R_{REF} the defining coordinate system of the mobile mechanical set (reference coordinate system)
- R_{A} the defining coordinate system of a particular position A of the mobile mechanical set
The R_{A} coordinate system is defined in relation with the R_{REF} coordinate system by means of the quantities presented in the table below.
Information | Description | |
---|---|---|
Position | Coordinates of the center of the R_{A} coordinate system in the R_{REF} coordinate system: (Xc, Yc, Zc) | |
Orientation | Components * of R_{A} coordinate system in the R_{REF} reference coordinate system: (Ux, Uy, Uz), (Vx, Vy, Vz) (Wx, Wy, Wz) |
Complements
Let us consider:
- three unitary orthogonal vectors Ex, Ey, Ez and an origin O defining the initial coordinate system (of reference) of the mechanical set: R_{REF}
- three unitary orthogonal vectors E1, E2, E3 and an origin C defining the position A of the mechanical set: R_{A}
The second coordinate system is known in the first one, which means that the triplets (Ux, Uy, Uz), (Vx, Vy, Vz) et (Wx, Wy, Wz) are known as:
E1 = Ux*Ex + Uy*Ey + Uz*Ez
E2 = Vx*Ex + Vy*Ey + Vz*Ez
E3 = Wx*Ex + Wy*Ey + Wz*Ez