/HA3Dynamics-

HA 3 Dynamics

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HA3Dynamics-

Jacobians, Trajectories of manipulator!!!

Task 1: {#task-1 .unnumbered}

Derive FK equations for the robot depicted in figure [fig:mesh1]. Use $\theta_1$, $\theta_2$, $d_3$ as joint space variables, $p_x$, $p_y$, $p_z$ as operational space variables. Parameters $d_1$, $a_2$ are known (assign them some positive values for succeeding tasks).

RRP robot. [fig:mesh1]

Task 2 {#sec:Task 2 .unnumbered}

Derive IK equations.

Task 3: {#task-3 .unnumbered}

Compute the manipulator Jacobian for representation of linear and angular velocity of point p.

  • Use classical approach (partial derivatives).

  • Use geometric approach (cross products).

Task 4: {#task-4 .unnumbered}

Analyze the Jacobian for singularities. Characterize each singular configuration if any.

Task 5: {#task-5 .unnumbered}

Compute the velocity of the tool frame when joint variables are changing with time as follows:

$\theta_1(t) = sin(t)$, $\theta_2(t) = cos(2t)$, $d_3(t) = sin(3t)$.

Add some fancy graphs showing evolution of all variables

Task 6: {#task-6 .unnumbered}

Let tool coordinates changing with time as follows:

$p_x(t) = 2a_2sin(t)$, $p_y(t) = 2a_2cos(2t)$, $p_z(t) = d_1sin(3t)$

Determine a feasible joint trajectory for this tool trajectory.

  • Use IK solution.

  • Use inverse differential kinematics approach. Consider only linear velocity part of Jacobian.

test