Module 1   :   Dynamics of Rigid Bodies in Plane Motion; Dynamic Force Analysis of Machines
Lecture 1 :   Dynamics of Rigid Bodies in Plane Motion; Dynamic Force Analysis of  Machines.

Joint Reactions

 

A mechanism consists of bodies which are connected together by kinematic pairs. One approach to derive the equations of motion for mechanisms (called Newton-Euler approach) considers each body as a free body, along with the forces due to the constraints, called joint reactions. We use this approach here. First, let us consider the nature of joint reactions for different types of joints.                            
  Revolute Joint:
  Two bodies connected by a revolute joint are shown in Fig. 1.2(a) and the free body diagrams of the two bodies are shown in Fig. 1.2(b). The revolute joint prevents the two bodies from undergoing relative translational motion along say x and y. Hence, the reaction force is represented by two components, and . The reaction forces on the two bodies are equal and opposite, as required by Newton 's third law.
 

Fig. 1.1.2 Revolute Joint
  Prismatic Joint:
  Two bodies connected by a prismatic joint are shown in Fig. 1.3(a) and the free body diagrams of the two bodies are shown in Fig. 1.3(b). The prismatic joint prevents relative translation in a direction normal to the line of the joint and also relative rotation. Hence, the reaction forces are represented by normal reaction force   and couple . The point at which acts is usually fixed to the piston and moves with the piston. The position of   is not important, however, the direction of   has to be normal to the direction of relative translation between the two bodies. The reaction forces and couples on the two bodies are equal and opposite, as required by Newton 's third law.
 

Fig. 1.1.3 Prismatic Joint
   
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