ElmoMC Multi-Axis Motion Controller-Maestro Motion Control User Manual

Page 3

Contents

Chapter 1: General Description ..............................................................................................

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 .............

1.3.3.2 Examples of three-dimensional spline interpolation ...................

1.3.4 Polyline ............................................................................................. 10

1.3.4.1 Examples for the two-dimensional polyline ...............................

1.3.4.2 Examples for the three-dimensional polyline.............................

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)