I am trying out the serial chain manipulator example
<https://docs.sympy.org/latest/modules/physics/mechanics/examples/multi_degree_freedom_holonomic_system.html>
in the sympy mechanics docs but am finding out that the kinematics sympy
computes in the backend are buggy. I am attaching the file I use to test
it. In the example
<https://docs.sympy.org/latest/modules/physics/mechanics/examples/multi_degree_freedom_holonomic_system.html>,
the velocity of the center of mass of the simple pendulum *should be :
u1(t)*N_frame.x + l*u2(t)*B_frame.x + l*(u2(t) + u3(t))*C_frame.x*.
However, *sympy returns : u1(t)*N_frame.x + l*u3(t)/3*B_frame.x +
l*u3(t)*C_frame.x*.
I tried to investigate this by looking at the definition of a PinJoint in
sympy. It turns out every joint, when initialized calls the
*_set_linear_velocity* function. In case of the PinJoint the
*_set_linear_velocity* function calls
*child.masscenter.v2pt_theory(parent.masscenter,
parent.frame, child.frame)* to impose velocity constraints between the
child and parent link mass centers. The v2pt_theory function operates under
the assumption that child and parent mass centers are fixed in the child
frame (frame attached to the center of mass of the child). This would hold
true if the parent link has mass concentrated at one end (or at the joint
i.e. COM and joint location coincide) but not if the joint location is
anywhere other than the COM of the parent link.
Is there a way to define a serial chain manipulator in sympy without making
such assumptions about the mass distribution of the links?
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from sympy import zeros, symbols
from sympy.physics.mechanics import Body, PinJoint, PrismaticJoint, JointsMethod, inertia
from sympy.physics.mechanics import dynamicsymbols
from ipdb import set_trace
q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1, q2, q3, u1, u2, u3')
l, k, c, g, kT = symbols('l, k, c, g, kT')
ma, mb, mc, IBzz= symbols('ma, mb, mc, IBzz')
wall = Body('N')
block = Body('A', mass=ma)
IB = inertia(block.frame, 0, 0, IBzz)
compound_pend = Body('B', mass=mb, central_inertia=IB)
simple_pend = Body('C', mass=mc)
bodies = (wall, block, compound_pend, simple_pend)
slider = PrismaticJoint('J1', wall, block, coordinates=q1, speeds=u1)
rev1 = PinJoint('J2', block, compound_pend, coordinates=q2, speeds=u2,
child_axis=compound_pend.z, child_joint_pos=l*2/3*compound_pend.y,
parent_axis=block.z)
rev2 = PinJoint('J3', compound_pend, simple_pend, coordinates=q3, speeds=u3,
child_axis=simple_pend.z, parent_joint_pos=-l/3*compound_pend.y,
parent_axis=compound_pend.z, child_joint_pos=l*simple_pend.y)
joints = (slider, rev1, rev2)
print(simple_pend.masscenter.vel(wall.frame))
# set_trace()
