kins.txt

/*
                 _
4-wire planar 2-RPR parallel robot

Translational motion is only allowed using constant zero degrees of end-effector rotation.  If angular rotation is allowed the forward kinematics requires a 6th degree roots solve, but only quadratic without.

-- anchor points (Lx by Ly square) --
A1 = {0, 0}
A2 = {0, Ly}
A3 = {Lx, 0}
A4 = {Lx, Ly}

-- end-effector attachment points (b by h square) --
B1 = {-b/2.0, -h/2.0}
B3 = {b/2.0, -h/2.0}

-- joint 0 and 2 lengths --
L1 and L3 input

x,y = the intersection of 2 circles that are offset by the constant B1,B3 and having radius equal to the joint length

circle_intersect( A1-B1, L1, A3-B3, L3 )
                ( {b/2.0, h/2.0}, L1, {-b/2.0) + Lx, h/2.0}, L3 )

take positive solution, ie 1st

*/

/*

A1 = {0, 0}
A2 = {0, Ly}
A3 = {Lx, 0}
A4 = {Lx, Ly}

-- A2 *__                                ______* A4
 ^       \__L2                    __L4__/
 |           \___     b    ______/
 |               *--------*
Ly               |        | h
 |            ___*--------*______
 |        ___/                   \______
 v     __/ L1                       L3  \______
-- A1 *                                        * A3
      |<-------------- Lx -------------------->|



L1 = Sqrt[Abs[0.5 b - x]^2 + Abs[0.5 h - y]^2]

L2 = Sqrt[Abs[0.5 b - x]^2 + Abs[-0.5 h + Ly - y]^2]

L3 = Sqrt[Abs[-0.5 b + Lx - x]^2 + Abs[0.5 h - y]^2]

L4 = Sqrt[Abs[-0.5 b + Lx - x]^2 + Abs[-0.5 h + Ly - y]^2]

*/