first upload

Author: oselin

DAE.mlx

@@ -0,0 +1,39 @@
+
+with(MBSymba_r6):
+
+draw_mech := proc(sol::{list(`=`),set(`=`)}, data::{list(`=`),set(`=`)}, dof)
+
+          local p0,p1,p2,p3,p3b,p4,p5,rRj,g3,p_act;
+          rRj := 0.002: # radius of joint symbols
+
+          p0  := evalf(subs(sol,data,dof, [comp_XYZ(P0,  ground)])):
+          p1  := evalf(subs(sol,data,dof, [comp_XYZ(P1,  ground)])):
+          p2  := evalf(subs(sol,data,dof, [comp_XYZ(P2,  ground)])):
+          p3  := evalf(subs(sol,data,dof, [comp_XYZ(P3,  ground)])):
+          p3b := evalf(subs(sol,data,dof, [comp_XYZ(P3b, ground)])):
+          p4  := evalf(subs(sol,data,dof, [comp_XYZ(P4,  ground)])):
+          g3  := evalf(subs(sol,data,dof, [comp_XYZ(Gflap,  ground)])):
+          p5  := evalf(subs(sol,data,dof, [comp_XYZ(P5,  ground)])):
+          p_act := evalf(subs(sol,data,dof, [x1,y1])):
+
+          display(   #plottools:-disk(p0[1..2],rRj,color="Yellow"),
+                     plottools:-disk(p1[1..2],rRj,color="Orange"),
+                     plottools:-disk(p2[1..2],rRj,color="Red"),
+                     plottools:-disk(p3[1..2],rRj,color="Violet"),
+                     plottools:-disk(p3b[1..2],rRj,color="Violet"),
+                     plottools:-disk(p4[1..2],rRj,color="Violet"),
+                     plottools:-disk(g3[1..2],rRj,color="Violet"),
+                     plottools:-disk(p5[1..2],rRj,color="Violet"),
+                     
+                     #plottools:-line(p0[1..2],p1[1..2],thickness=1,color="orange"),
+                     plottools:-line(p1[1..2],p2[1..2],thickness=3,color="DodgerBlue"),
+                     plottools:-line(p2[1..2],p3[1..2],thickness=3,color="orange"),
+                     plottools:-line(p4[1..2],p5[1..2],thickness=3,color="Violet"),
+                     plottools:-line(p4[1..2],p3b[1..2],thickness=3,color="Violet"),
+                     plottools:-line(p_act[1..2],p1[1..2],thickness=5,color="Red"),
+                     plottools:-polygon([p4[1..2],p5[1..2],g3[1..2]],color="Violet"),
+                     
+                     
+          scaling = constrained,size=[800,300]);
+          
+end proc:

DRS_DAE2.m

@@ -0,0 +1,92 @@
+
+with(MBSymba_r6):
+with(LinearAlgebra):
+
+# GLOBAL APPROACH
+P0   := origin(ground):
+P011 := make_POINT(ground,x1,y1,0):
+P40  := make_POINT(ground,x4,y4,0):
+
+printf("\nReference frame 1"):  
+RF1  := combine(translate(x0(t),y0(t),0).rotate('Z',theta0(t))):
+P01  := origin(%):
+Gact := make_POINT(RF1,(s(t)+L1)/2,0,0):
+P1   := make_POINT(RF1,s(t),0,0):
+P2   := make_POINT(RF1,s(t)+L1,0,0):
+print(RF1):
+
+
+
+printf("\nReference frame 2"):  
+RF2  := combine(translate(x2(t),y2(t),0).rotate('Z',theta1(t))):
+Gpod := origin(%):
+P22  := make_POINT(RF2,-LP/2,0,0):
+P3   := make_POINT(RF2, LP/2,0,0): 
+print(RF2):
+
+printf("\nReference frame 3"):  
+RF3 := combine(translate(x3(t),y3(t),0).rotate('Z',theta3(t))):
+P4  := origin(%):
+P3b := make_POINT(RF3,anc,0,0):
+P5  := make_POINT(RF3,LF,0,0):
+Gflap := make_POINT(RF3.rotate('Z',psi),LFb,0,0):
+print(RF3):
+
+# Constraint equations
+# Constraint equations : prismatic joint in P1
+join_points(P011,P01):                            
+Phi1 := map(simplify,[comp_X(%,ground),comp_Y(%,ground)]):
+
+# Constraint equations : revolute joint in P2
+join_points(P2,P22):                              
+Phi2 := map(simplify,[comp_X(%,ground),comp_Y(%,ground)]):
+
+# Constraint equations : revolute joint in P3
+join_points(P3,P3b):                              
+Phi3 := map(simplify,[comp_X(%,ground),comp_Y(%,ground)]):
+
+# Constraint equations : revolute joint in P4
+join_points(P4,P40):                              
+Phi4 := map(simplify,[comp_X(%,ground),comp_Y(%,ground)]):
+
+# Constraint equations: prismatic joint in RF1
+Phi5 := [dot_prod(uvec_Y(RF1),uvec_X(ground))]:
+
+# Assembling the constraint equations
+printf("\nThe constraint equations are"):  
+Phi := Phi1 union Phi2 union Phi3 union Phi4 union Phi5: print(<Phi>):
+
+# Define the list of variables
+printf("\nKinematics variables"):  
+q_vars := {theta0(t),theta1(t),theta3(t),s(t),x0(t),y0(t),x2(t),y2(t),x3(t),y3(t)}:
+print(%):
+# Check the DOFs of the system
+# Check jacobian of constraints for consistency
+printf("\nCheck the consistency of the system (Implict function theorem)"):
+combine(jacobianF(Phi, q_vars));  Dimensions(%);
+combine(GaussianElimination(%%)); Dimensions(%);
+
+# the system is consistent so i can apply the general formula to compute the degree of freedom of a body
+;
+# Number of degree of freedom
+nq := nops(q_vars):
+nc := nops(Phi):
+
+printf("\nThe DOFs of the system are"):
+n_dof = nq - nc;
+# Analytic solution
+q_I := {theta3(t)}:
+q_D := q_vars minus q_I;
+
+printf("Analytic solution"):
+sol_kine_all := op(solve(Phi, convert(q_D,list), explicit=true)): <%>;
+
+printf("Let's find the right configuration, evaluating the solutions for %a=%f",theta3(t),flap_closed):
+evalf(subs(data,param_not_opt, theta3(t)=flap_closed, sol_kine_all[1]));
+evalf(subs(data,param_not_opt, theta3(t)=flap_closed, sol_kine_all[2]));
+evalf(subs(data,param_not_opt, theta3(t)=flap_closed, sol_kine_all[3]));
+evalf(subs(data,param_not_opt, theta3(t)=flap_closed, sol_kine_all[4]));
+
+sol_kine := sol_kine_all[1]:
+read("./lib/kinematics/OPTIMIZATION.maplet"):
+read("./lib/kinematics/PVAanalysis.maplet"):