ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 3)

Contents
Chapter 1: General Description .............................................................................................. 1
1.1 Introduction ............................................................................................................ 1
1.2 Vector properties ...................................................................................................... 1
1.3 Trajectory generation ............................................................................................... 3
1.3.1 Line................................................................................................................ 3
1.3.2 Circle ............................................................................................................. 3
1.3.3 Spline............................................................................................................. 3
1.3.3.1 Examples for the two-dimensional spline interpolation ............. 5
1.3.3.2 Examples of three-dimensional spline interpolation ................... 6
1.3.4 Polyline ............................................................................................. 10
1.3.4.1 Examples for the two-dimensional polyline ............................... 12
1.3.4.2 Examples for the three-dimensional polyline............................. 14
1.4 Transition to a new trajectory with a non-zero velocity..................................... 16
Chapter 2: Switch Radius Calculation ................................................................................ 2-1
2.1 Line – line intersection .......................................................................................... 2-1
2.2 Circle – line intersection ....................................................................................... 2-6
2.2.1 Line goes inside the circle ............................................................... 2-6
2.2.1.1 Switch arc center and circle center belong to two different half
planes defined by the line L ...................................................................
2-6
2.2.1.2Switch arc center and a circle center belong to the same half
plane………............................................................................................
2-12
2.2.1.3 Line intersects the center of the circle...................................... 2-17
2.2.2 Switch arc radius calculation by the distance from the intersection
point …………………………………………………………………….2-
20
2.2.2.1 Initial circle center and switch arc center belong to the same
half-plane ...............................................................................................
2-20
2.2.2.2 Initial circle center and switch arc center belong to two half
planes defined by the line L. ................................................................
2-22
2.2.2.3 Circle center (Xc,Yc) Є L1 (line L1 intersects the center of the
circle)…................................................................................................... 2-24
2.2.3 Line goes outside the circle .................................................................. 2-24
2.2.3.1 Line L and init radius continued in their positive intersecting
directions................................................................................................
2-25
2.2.3.2 Line parallel to the circle arc init radius ....................................... 2-27
2.2.3.3 Line L and init radius continued in their reverse directions intersect 2-28
2.3 Circle – circle intersection.................................................................................. 2-30
2.3.1 One of two circle arcs intersects the internal area of the second...... 2-31
2.3.2 Each circle intersects the internal area of the second......................... 2-39
2.3.3 No circle intersects the internal area of the other .............................. 2-42
Appendix A: Projection of a point on a line defined by the end points ........................ A-1
Appendix B: Coefficients of the line standard equation for the line defined by the end
points ........................................................................................................................................B-1
Appendix C: Intersection point of two lines defined by the end points ....................... C-1
Appendix D: Circle – line intersection points ................................................................... D-1
Motion Library Tutorial
MAN-MLT (Ver 2.0)