Kennedy’s Theorem—A Practical Approach

In Chap.  3 we used vectors and trigonometry to find displacement, velocity, and accelerations for an in-Line and offset slider crank mechanism. We applied the same vector and trigonometric approach in chapter four to calculate the displacement and velocity for 4-bar mechanisms. In this chapter we will introduce two concepts that allows us to solve for linear and angular velocities. First we define: Instantaneous Centers (IC): A point in space where only rotation occurs. Students should note the term “in space” since an IC does not need to reside on the link. Kennedy’s Theorem: When 3 bodies are in motion relative to each other there will be 3 ICs all lying on a straight line. To find the instantaneous centers we start with the circle diagram in Fig. 5.1. The circle is applicable to the slider crank and 4-bar mechanisms. The solid lines (1–2), (2–3), (3–4), and (1–4) represents ICs. Students should notice that points (1–2), (2–3), and (3–4) are the pin connections. For a slider crank mechanism the IC for the frame (point 1) and slider (point 4) is a line perpendicular to its line of action and extends to infinity. The ICs (2–4) and (1–3) are represented by the dotted lines and Kennedy’s theorem will identify their location.