HCR ~ Exam 2017-02-27 (with Solutions)

• Exercise 1: Linear Algebra ^exercise-1
  • Find the solution(s) of this linear system:$Ax=y$Where:$A=\left[\begin{array}{lcc}2& 3& 4\\ 0& 1& 0\\ 1& 0& 0\end{array}\right],y=\left[\begin{array}{l}1\\ 2\\ 2\end{array}\right]$Tip: Solve the problem using the concept of RANK of matrices and discuss how many solutions the system has.
• Exercise 2: Grasping
  • Discuss how to equilibrate external wrenches $w$ applied on the object with a grasp matrix having matrix $G$. How do you choose contact forces in $\omega =-G\lambda$.
    Assume that the grasp has 3 hard finger contacts.
• Exercise 3: Haptics
  • (a) What are the triangular meshes of a surface?
  • (b) Why you use the concept of interpolation?
  • (c) Discuss the multiple fingers interaction.

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• Solutions
  • (Exercise 1: Linear Algebra)TODONOT_SURE_ABOUT_THIS I will give my response, I don't know if its correct, I don't understand the one given in the PDFs
    First we find the determinant of the matrix $A$ using the rule of Sarrus, then if the determinant is $0$ we will say that the rank of the matrix is NOT full, so it will not exist a solution for the linear equation.
    While if $\det (A)\ne 0$, then we will say that $A$ has full rank, so it is invertible and the solution can be found by solving the following equation:$y=A^{-1}x$
  • (Exercise 2: Grasping) ⇒ Same as: exam (2017 04 04).
  • (Exercise 3: Haptics - a.)TODO
  • (Exercise 3: Haptics - b.)TODO
  • (Exercise 3: Haptics - c.)TODO

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Original Files

• Exam:
  
• Solutions: