Question

Figure 2. A three-link planar arm and its frame assignments 3. Consider the planar arm described in Figure 2. i) Determine the DH parameters of the three joints and derive homogeneous transformation matrices $^i_{-1}T_i$, $i = 1, 2, 3$, and $^3T_H$. (15pts) ii) Use Symbolic MATLAB to derive the forward-pose kinematics solution $^0T_H$. (10pts) iii) Calculate the forward-pose kinematics results via MATLAB for the following input cases: $\theta_1 = 30^\circ$, $\theta_2 = 60^\circ$, $\theta_3 = 30^\circ$, $L_1 = 4$, $L_2 = 3$, and $L_3 = 2$ (m) (5pts) iv) Derive the inverse kinematics of the planar arm, that is, given $(x, y, \theta)$, find the solutions of $(\theta_1, \theta_2, \theta_3)$. (10pts)

          Figure 2. A three-link planar arm and its frame assignments
3. Consider the planar arm described in Figure 2.
i) Determine the DH parameters of the three joints and derive homogeneous
transformation matrices $^i_{-1}T_i$, $i = 1, 2, 3$, and $^3T_H$. (15pts)
ii) Use Symbolic MATLAB to derive the forward-pose kinematics solution $^0T_H$.
(10pts)
iii) Calculate the forward-pose kinematics results via MATLAB for the following
input cases: $\theta_1 = 30^\circ$, $\theta_2 = 60^\circ$, $\theta_3 = 30^\circ$, $L_1 = 4$, $L_2 = 3$, and $L_3 = 2$ (m) (5pts)
iv) Derive the inverse kinematics of the planar arm, that is, given $(x, y, \theta)$, find
the solutions of $(\theta_1, \theta_2, \theta_3)$. (10pts)

Figure 2. A three-link planar arm and its frame assignments
3. Consider the planar arm described in Figure 2.
i) Determine the DH parameters of the three joints and derive homogeneous
transformation matrices ^i-1Ti, i = 1, 2, 3, and ^3TH. (15pts)
ii) Use Symbolic MATLAB to derive the forward-pose kinematics solution ^0TH.
(10pts)
iii) Calculate the forward-pose kinematics results via MATLAB for the following
input cases: θ1 = 30^∘, θ2 = 60^∘, θ3 = 30^∘, L1 = 4, L2 = 3, and L3 = 2 (m) (5pts)
iv) Derive the inverse kinematics of the planar arm, that is, given (x, y, θ), find
the solutions of (θ1, θ2, θ3). (10pts)

Added by Fernando G.

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