1: Intro: Terms and Degrees of Freedom Tuesday, March 8, 2022 11:35 AM Solid Mechanics One subdivision of Mechanical Engineering as a discipline is Mechanics, or Solid Mechanics. It can be further subdivided as shown: Statics This course focuses chiefly on kinematics of several specific types of machine components (linkages, cams, gears, etc.). We will touch on some kinetics along the way. In fact, "Kinematics" is an alternative name for this course (used in some institutions). Stress Analysis Dynamics Kinematics Kinetics "___________ of motion" (one aspect of motion as it relates to other aspects of motion) "________ of motion" (effect of Forces/Moments on motion) Note that Kinetics and Kinematics actually are interdependent: no motion happens without a cause, and no aspect of motion is independent of all other aspects of motion. For example, a point's velocity is always related to its acceleration. The first part of this course focuses on __________ . Let's discuss a few terms and definitions. ______ : A body that can be connected to other bodies. Think of a flat bar with a hole at each end, that can be _________ to other flat bars. ______________ ________ : A series of links joined together _____________ : A kinematic chain where at least one link is grounded/fixed. __________ : A mechanism designed to transmit significant force/energy. Degrees of Freedom (or, __________ ) Two definitions are given for a system's degrees of freedom (DOF): - The number of independent _____________ needed to define the position of a system - The number of independent _____ a system can move These definitions communicate the same idea from two different perspectives. How many DOF's does an unconstrained body in 2-D space have? What about 3-D space? Tip: it is helpful to name or describe the DOF's. ("horizontal translation", "rotation about the z-axis", etc.) For _____________ motion, a mechanism requires as many independent inputs as it has DOF's. Thus, we need to be able to assess the number of DOF's a system has. This task can be challenging for a complicated mechanism, with many bodies and joints; so let's look at a process for assessing a system's DOF's. Links can be described by the number of ______________ they have. Note that adding an unused hole would not change the link's status, only adding a connection would. Types of 2D joints: Full joints: they remove ___ DOF, leaving ___ DOF (of one body relative to the other body). Half joints: they remove ___ DOF, leaving ___ DOF (relative) Joint closure (independent of whether it is a full or half joint) - A force-closed joint can only transmit force in one direction without separating. - A form-closed joint can transmit force in both directions without separating. Adding multiple bodies to a single joint is the same as adding ________ joint; each extra body in the joint removes more DOF's. A rolling joint is special; it may be a full joint or a half joint. To distinguish, we must know whether there is _____ at the rolling joint. - Rolling ________ slip = full joint; 1 DOF remains: - Rolling _____ slip = half joint; 2 DOF remain: The number of DOF's of a system depends on the assumptions we make. As an example, let's consider a unicycle. Some key assumptions are: - Are we considering motion in ___ or ___ ? - How many/which ______ are we considering? - How is the cycle being ___________ ? The answers to these questions drastically affect the number of DOF's we will identify. Suppose we assume the following: - ___ motion - __ bodies - No _________ or wheel ____ Discuss: How many DOF's can you identify? State your assumptions, then try to name/describe all the DOF's under those assumptions. Intuitively, we can conclude that there are __ DOF's: We also can arrive at the same conclusion mathematically: This line of thinking is known as ___________ logic. For more complicated systems with motion that is difficult to visualize, it can enable us to properly asses the number of DOF's. In equation form, it is known as the __________ equation: Find the mobility of the following: Clearly the system can move… what went wrong? A situation like this (where the Kutzbach equation is incorrect) is called a __________ . It occurs when there is ____________ in the way the DOF's are counted.
