(Solved): In our experiments, we created a virtual wall whose reaction force formulatio ...

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In our experiments, we created a virtual wall whose reaction force formulation was defined as \( F=k \Delta x \), where " \( k \) " is the stiffness value and \( \Delta x \) is deflection. Let's assume that we intend to create such a virtual wall that it is at \( x=30 \mathrm{~mm} \) and above. Take \( k=3 \mathrm{kN} / \mathrm{m} \). ( 30 pts.) a. Calculate reaction force if the end-effector's position \( (x, y) \) is \( (10 \mathrm{~mm}, 32 \mathrm{~mm}) \). Explain briefly. b. Calculate reaction force if the end-effector's position \( (x, y) \) is \( (32 \mathrm{~mm},-20 \mathrm{~mm}) \). Explain briefly. c. Can we make the stiffness value converge to infinity? Why? Explain.