ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 26)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-5
Line 1 is defined by its init point (300000, 900000) and end point (700000,200000). Line 2 is
defined by the init point (700000,200000) and its end point (1100000,700000). Switch from
Line 1 to Line 2 must be executed with a distance from the intersection point pre-defined by
the user vsc = 3, vsd = 20000. We define cruise velocity vsp = 50000 and end velocity vse =
50000. Vector acceleration/deceleration vac = vdc = 28000000
1. We calculate the minimal switch radius that satisfies the kinematics constraint
r_min = (vse) 2 /(vac*vae) = (50000) 2 /(28000000*0.9) = 99.2
2. Geometric description of the two lines intersecting:
ΔX
1
= X
12
– X
11
= 700000 - 300000 = 400000
ΔY
1
= Y
12
– Y
11
= 200000 – 900000 = -700000
ΔX
2
= X
22
– X
21
= 1100000 – 700000 = 400000
ΔY
2
= Y
22
– Y
21
= 700000 – 200000 = 500000
The length of the first line segment
ΔL
1
= [ΔX
12
+ ΔY
1 2
] 1/2 = [400000 2 + (-700000)
2
] 1/2 = 806225.8
The length of the second line segment
ΔL
2
= [ΔX
22
+ ΔY
12
] 1/2 = [400000 2 + 500000 2 ] 1/2 = 640312.4
Notice that d < ΔL
1
and d < ΔL
1
An angle between the two lines can be calculated as
γ = π – arcos[(ΔX
1
ΔX
2
+ ΔY
1
ΔY
2
)/( ΔL
1
ΔL
2
)] =
= π – arcos{[400000*400000 + (-700000)( 500000)]/(806225.8*640312.4)}=
1.193887 = 68.4
o
The switch radius corresponding to the given d can be calculated as
r=d*tg(γ/2) = 20000tg(0.5*1.193887) = 13593
1. Check the kinematics constraints. A minimal switch radius that fits kinematics
constraints can be calculated as
r
min
> vse*vse/(vac*vae) = 50000 2 /(28000000*0.9) = 99.2
The implicitly pre-defined switch radius is 13593 >>
r
min.
A number of similar examples with a different set of user defined and calculated
parameters are considered in the Motion Mathematic Lib Samples examples
TwoLinesFixDist_Fx2D_1 - TwoLinesFixDist_Fx2D_2.