[SOLVED] Cmpsci 403: introduction to robotics: perception, mechanics, dynamics, and control hw 02

1. How many degrees of freedom (n) does this mechanism possess?
2. Where would you attach motors to control the position of the end effector in the plane?
3. Based on your choice, define joint position vectors q ∈ R
n and derive forward kinematic equations
that relate the inputs (motor angles) to the outputs (end effector position in Cartesian coordinate, i.e.
p = (x, y)).
4. Obtain the Jacobian matrix J(q) = dp
dq symbolically in Matlab.
5. Use this Jacobian to relate output forces (Fx, Fy) at the tip of the arm to statically equivalent input
torques (τ1, τ2).
Assumptions and tips:
• You should define fixed parameters as necessary.
• You can assume that the linkage is a parallelogram.
• Consider using Matlab functions: syms, eval, jacobian
• You may want to read the Matlab Symbolic Computation Toolbox Tutorial before getting started:
http://www.mathworks.com/help/symbolic/performing-symbolic-computations.html
Ground
y
x
(Fx , Fy) p(q) = (x, y)
End effector
1