Shear Press - Kinematics Model

Kinematic Model

points definition

> A := make_POINT(ground,0,0,0): show(A); frame pin joint

> B := make_POINT(ground,xB,yB,0): show(B);

> xC := d; constan value
C := make_POINT(ground,xC,yC,0): show(C); slider

> P := make_POINT(ground,xP,yP,0): show(P);

variables

> q := { xB,yB,yC,xP,yP }; nq := nops(q);

Since the single-degree-of-freedom mechanism is described by means of 5 variables,
4 constraint equations must be written. All they correspond to the lenght of constant segments

> AB := make_VECTOR(A,B): phi[1] := dot_prod(AB,AB)-lAB^2;

> BC := make_VECTOR(B,C): phi[2] := dot_prod(BC,BC)-lBC^2;

> AP := make_VECTOR(A,P): phi[3] := dot_prod(AP,AP)-lAP^2;

> BP := make_VECTOR(B,P): phi[4] := dot_prod(BP,BP)-lBP^2;

> phi:=convert(phi,list):

Numerical solution (Newton-Rapson algorithm)

mechanims characteristics

> geometric_data := lAB=0.230, lBP=0.450, lBC=0.250+.15, lAP=0.650, d=0.27;

numerical equations

> eqns := convert(subs(geometric_data,phi),set);

definition of the independent variable and unknowns variables

> yP;
unks := q minus {%};

numerical solution

> np:=9: solz:=array[np]:
for i from 1 to np do
x := 0.5-0.2*(i-1)/(np-1):
solz[i] := {yP=x, d=subs(geometric_data,d) } union
fsolve(subs(yP=x,eqns),unks, {xP=0..1, yC=-1..0.1, xB=0..0.15})
end do:

tabbed results

> printf(" | xP yP | xB yB | xC yC |");
for i from 1 to np do
printf("%2.0f | %+06.3f %+06.3f | %+06.3f %+06.3f | %+06.3f %+06.3f |",
i ,op( subs(solz[i],geometric_data, [xP,yP,xB,yB,d,yC])));
writeline(default):
end do:

   |     xP      yP   |     xB      yB   |    xC     yC    |

 1 |  +0.415  +0.500  |  +0.062  +0.222  |  +0.270 -0.120  |

 2 |  +0.444  +0.475  |  +0.075  +0.218  |  +0.270 -0.131  |

 3 |  +0.469  +0.450  |  +0.086  +0.213  |  +0.270 -0.142  |

 4 |  +0.492  +0.425  |  +0.097  +0.208  |  +0.270 -0.152  |

 5 |  +0.512  +0.400  |  +0.108  +0.203  |  +0.270 -0.162  |

 6 |  +0.531  +0.375  |  +0.117  +0.198  |  +0.270 -0.172  |

 7 |  +0.548  +0.350  |  +0.126  +0.192  |  +0.270 -0.181  |

 8 |  +0.563  +0.325  |  +0.135  +0.186  |  +0.270 -0.190  |

 9 |  +0.577  +0.300  |  +0.143  +0.180  |  +0.270 -0.199  |

mechanism drawing

> with(plots): with(plottools):

> draw_mechanism := proc(q)
local revj_A,revj_B,revj_C, mech,lever,rod,blade,guide:
revj_A := disk([ 0, 0], 0.02, color=yellow);
revj_B := disk(subs(q,[xB,yB]), 0.02, color=yellow);
revj_C := disk(subs(q,[xC,yC]), 0.02, color=yellow);
lever := polygon(subs(q,[[0,0],[xB,yB],[xP,yP]]), color=green, thickness=1);
rod := line( subs(q,[xB,yB]),subs(q,[xC,yC]), color=black, thickness=5);
blade := polygon(subs(q,[[xC+0.03,yC+0.03],[xC-0.03,yC+0.03],[xC-0.03,yC-0.05],[xC+0.03,yC-0.13]]), color=blue, thickness=1);
guide := rectangle( subs(q,[xC+0.03, 0]), subs(q,[xC+0.13, -0.4]), color=grey ):

mech := rod,guide,revj_A,revj_B,revj_C,blade,lever;
end:

Warning, the name arrow has been redefined

Warning, the name arrow has been redefined

display a single configuration

> #display(draw_mechanism(solz[1]), scaling=constrained);

animation

> display([seq(display(draw_mechanism(solz[i])),i=1..np)], insequence=true, scaling=constrained);

>