Geometric Primitives

Geometric primitives are represented by the following classes.

**Twist and Wrench transformations**- 3 different types of transformations do exist for the twists and wrenches.

* 1) Frame * Twist or Frame * Wrench : * this transforms both the velocity/force reference point * and the basis to which the twist/wrench are expressed. * 2) Rotation * Twist or Rotation * Wrench : * this transforms the basis to which the twist/wrench are * expressed, but leaves the reference point intact. * 3) Twist.RefPoint(v_base_AB) or Wrench.RefPoint(v_base_AB) * this transforms only the reference point. v is expressed * in the same base as the twist/wrench and points from the * old reference point to the new reference point. *

**Warning:**- Efficienty can be improved by writing p2 = A*(B*(C*p1))) instead of p2=A*B*C*p1

**PROPOSED NAMING CONVENTION FOR FRAME-like OBJECTS**

* A naming convention of objects of the type defined in this file : * (1) Frame : F... * Rotation : R ... * (2) Twist : T ... * Wrench : W ... * Vector : V ... * This prefix is followed by : * for category (1) : * F_A_B : w.r.t. frame A, frame B expressed * ( each column of F_A_B corresponds to an axis of B, * expressed w.r.t. frame A ) * in mathematical convention : * A * F_A_B == F * B * * for category (2) : * V_B : a vector expressed w.r.t. frame B * * This can also be prepended by a name : * e.g. : temporaryV_B * * With this convention one can write : * * F_A_B = F_B_A.Inverse(); * F_A_C = F_A_B * F_B_C; * V_B = F_B_C * V_C; // both translation and rotation * V_B = R_B_C * V_C; // only rotation *

**CONVENTIONS FOR WHEN USED WITH ROBOTS :**

* world : represents the frame ([1 0 0,0 1 0,0 0 1],[0 0 0]') * mp : represents mounting plate of a robot * (i.e. everything before MP is constructed by robot manufacturer * everything after MP is tool ) * tf : represents task frame of a robot * (i.e. frame in which motion and force control is expressed) * sf : represents sensor frame of a robot * (i.e. frame at which the forces measured by the force sensor * are expressed ) * * Frame F_world_mp=...; * Frame F_mp_sf(..) * Frame F_mp_tf(,.) * * Wrench are measured in sensor frame SF, so one could write : * Wrench_tf = F_mp_tf.Inverse()* ( F_mp_sf * Wrench_sf ); *

**CONVENTIONS REGARDING UNITS :**- Typically we use the standard S.I. units: N, m, sec.