Ronan

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Member for: 12 years, 210 days

Location: East Grinstead, United Kingdom

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2024 Wish List for MaplePrimes...

Posted: Ronan 1207 Product: MaplePrimes

January 01 2024

4 3

Happy new year everyone. Instead on making my usual new year resolutions, I though I would put up a request for some helpful improvements here.

1) Please make search work properly. Allow searches to target specific sections. Posts, Questions, My own account, Other users. etc,

2) Add links to Maple help. Is there an online way of viewing Maple document? Or build Maple viewer into this site.

3) Add links to Maple Learn.

Stewart Gough Reverse Kinematics...

Posted: Ronan 1207 Product: Maple 2017

June 03 2017

0 0

A question was raised recently on Stewart Gough platforms. I decided to tidy up some old code to show platform position and leg lengths for any given displacement.

Hexapod Setup Data

$RotZ := proc (delta) options operator, arrow; Matrix(1 .. 3, 1 .. 3, {(1, 1) = cos(delta), (1, 2) = -sin(delta), (1, 3) = 0, (2, 1) = sin(delta), (2, 2) = cos(delta), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1}, datatype = anything, storage = rectangular, order = Fortran_order, subtype = Matrix) end proc$

a[1] := Vector(3, [.5, 3.0, 0]); a[2] := evalf(RotZ(20*((1/180)*Pi)).a[1]); a[3] := evalf(RotZ(100*((1/180)*Pi)).a[2]); a[4] := evalf(RotZ(20*((1/180)*Pi)).a[3]); a[5] := evalf(RotZ(100*((1/180)*Pi)).a[4]); a[6] := evalf(RotZ(20*((1/180)*Pi)).a[5])

b[1] := evalf(.7*RotZ(-40*((1/180)*Pi)).a[1]); b[2] := evalf(RotZ(100*Pi*(1/180)).b[1]); b[3] := evalf(RotZ(20*Pi*(1/180)).b[2]); b[4] := evalf(RotZ(100*Pi*(1/180)).b[3]); b[5] := evalf(RotZ(20*Pi*(1/180)).b[4]); b[6] := evalf(RotZ(100*Pi*(1/180)).b[5])

Tx := Vector(3, [1, 0, 0]); Ty := Vector(3, [0, 1, 0]); Tz := Vector(3, [0, 0, 1])

Procedures

$PlatPosn := proc (x := 0, y := 0, z := 0, alpha := 0, beta := 0, delta := 0) local i, v, Rot, L1, L2, L3, L4, L5, L6; global txn, tyn, tzn, ctrp; description "Calculates the platform position in the Global Coordinates, Unit normals and Leg Lengths"; v := Vector(3, [x, y, z]); ctrp := Zeroposn+v; Rot := Matrix(1 .. 3, 1 .. 3, {(1, 1) = cos(delta)*cos(beta), (1, 2) = -sin(delta)*cos(alpha)+cos(delta)*sin(beta)*sin(alpha), (1, 3) = sin(delta)*sin(alpha)+cos(delta)*sin(beta)*cos(alpha), (2, 1) = sin(delta)*cos(beta), (2, 2) = cos(delta)*cos(alpha)+sin(delta)*sin(beta)*sin(alpha), (2, 3) = -cos(delta)*sin(alpha)+sin(delta)*sin(beta)*cos(alpha), (3, 1) = -sin(beta), (3, 2) = cos(beta)*sin(alpha), (3, 3) = cos(beta)*cos(alpha)}, datatype = anything, storage = rectangular, order = Fortran_order, subtype = Matrix); for i to 6 do bn || i := Zeroposn+v+Rot.b[i] end do; txn := Rot.Tx; tyn := Rot.Ty; tzn := Rot.Tz; print(" Platform centre Global", ctrp); print(" Platform corner Co-ords Global", bn1, bn2, bn3, bn4, bn5, bn6); print("Platform Triad Vectors ", "X green ", txn, "Y blue", tyn, "Z red ", tzn); L1 := sqrt((bn1-a[1])^%T.(bn1-a[1])); L2 := sqrt((bn2-a[2])^%T.(bn2-a[2])); L3 := sqrt((bn3-a[3])^%T.(bn3-a[3])); L4 := sqrt((bn4-a[4])^%T.(bn4-a[4])); L5 := sqrt((bn5-a[5])^%T.(bn5-a[5])); L6 := sqrt((bn6-a[6])^%T.(bn6-a[6])); print("Leg Lengths"); print("L1= ", L1); print("L2= ", L2); print("L3= ", L3); print("L4= ", L4); print("L5= ", L5); print("L6= ", L6) end proc$

(1)

(2)

tzn = Vector[column](%id = 18446744074564617750), `= `, Vector[column](%id = 18446744074328082542)

(3)

Rotation Matrices

RotZ := Matrix(3, 3, {(1, 1) = cos(delta), (1, 2) = -sin(delta), (1, 3) = 0, (2, 1) = sin(delta), (2, 2) = cos(delta), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

RotY := Matrix(3, 3, {(1, 1) = cos(beta), (1, 2) = 0, (1, 3) = sin(beta), (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = -sin(beta), (3, 2) = 0, (3, 3) = cos(beta)})

RotX := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(alpha), (2, 3) = -sin(alpha), (3, 1) = 0, (3, 2) = sin(alpha), (3, 3) = cos(alpha)})