Consider a joint between two rigid bodies. Each rigid body has mm degrees of freedom (m=3m=3 for a planar rigid body and m=6m=6 for a spatial rigid body) in the absence of any constraints. The joint has ff degrees of freedom (e.g., f=1f=1 for a revolute joint or f=3f=3 for a spherical joint). How many constraints does the joint place on the motion of one rigid body relative to the other? Write your answer as a mathematical expression in terms of m and f
Answers
Answer:
m-f
Explanation:
Answer:
The number of constraints that the joint imposes on one rigid body's motion in relation to another can be expressed as (m - f).
Explanation:
The motion of one rigid body concerning the other is somewhat constrained when they are joined by a joint. The number of degrees of freedom (DOF) that the joint permits defines this constraint.
A spherical joint offers three degrees of freedom, which correspond to rotation about all three axes (pitch, yaw, and roll).
A planar rigid body has 3 DOF (degrees of freedom) in the absence of any constraints, while a spatial rigid body has 6 DOF (three translations and three rotations). The amount of DOF that is available for the bodies to move freely is therefore decreased by the amount of DOF that the joint permits when a joint is added between two rigid bodies.
So, (m - f) can be used to represent mathematically how many constraints are placed on one rigid body's motion in relation to another.
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