(Solved): :5 The two degree of freedom manipulator is shown in the following figure. The transformation matr ...

:5 The two degree of freedom manipulator is shown in the following figure. The transformation matrices are also given. Derive the Jacobian matrix for the same. $${}^0{T}_1=\left[\begin{array}{cccc}{C}_1& ?S_1& 0& C_1\\ S_1& C_1& 0& S_1\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]{}^1{T}_2=\left[\begin{array}{cccc}{C}_2& ?S_2& 0& C_2\\ S_2& C_2& 0& S_2\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]$$ Q:6 The Articulated manipulator is shown in the following figure. The transformation matrices are also given. Derive the Jacobian matrix for the same. A 3-DOF articulated arm with three revolute joints $$\begin{array}{l}{}^0{T}_1=\left[\begin{array}{cccc}{C}_1& 0& S_1& 0\\ S_1& 0& ?C_1& 0\\ 0& 1& 0& 0\\ 0& 0& 0& 1\end{array}\right]{}^1{T}_2=\left[\begin{array}{cccc}{C}_2& ?S_2& 0& L_2{C}_2\\ S_2& C_2& 0& L_2{S}_2\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\\ {}^2{T}_3=\left[\begin{array}{cccc}{C}_3& ?S_3& 0& L_3{C}_3\\ S_3& C_3& 0& L_3{S}_3\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\end{array}$$ :7 The Stanford manipulator is shown in the following figure. Put the appropriate values in the given Jacobian of this manipulator.