1. A mechanism consisting of particles and rigid bodies has four degrees of freedom. What does this mean? 2. The generalized forces corresponding to a given applied force on a mechanism and relative to some chart are all zero. What does this mean? 3. What is the relationship between the rate of change of a potential energy function with respect to a coordinate function and the virtual work performed by the corresponding force during a small change in the coordinate function? 4. Suppose the generalized forces corresponding to a potential energy function are zero relative to some chart. Does this mean that the potential energy is constant for all possible con¯guration? Is it constant for all allowable con¯gurations? Explain your answer! 5. All curves in the collection of con¯gurations of a mechanism that belong to the same tangent vector are equivalent. What does this mean? 6. Give an example of two curves in the collection of allowable con¯gurations for some mechanism that intersect but are not equivalent! 7. Consider a tangent vector on the collection of allowable con¯gurations of some mechanism. Is this a
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