# Introduction to Mechanisms

Yi Zhang
with
Susan Finger
Stephannie Behrens

## 3 More on Machines and Mechanisms

### 3.1 Planar and Spatial Mechanisms

Mechanisms can be divided into planar mechanisms and spatial mechanisms, according to the relative motion of the rigid bodies. In a planar mechanisms, all of the relative motions of the rigid bodies are in one plane or in parallel planes. If there is any relative motion that is not in the same plane or in parallel planes, the mechanism is called the spatial mechanism. In other words, planar mechanisms are essentially two dimensional while spatial mechanisms are three dimensional. This tutorial only covers planar mechanisms.

### 3.2 Kinematics and Dynamics of Mechanisms

Kinematics of mechanisms is concerned with the motion of the parts without considering how the influencing factors (force and mass) affect the motion. Therefore, kinematics deals with the fundamental concepts of space and time and the quantities velocity and acceleration derived there from.

Kinetics deals with action of forces on bodies. This is where the the effects of gravity come into play.

Dynamics is the combination of kinematics and kinetics.

Dynamics of mechanisms concerns the forces that act on the parts -- both balanced and unbalanced forces, taking into account the masses and accelerations of the parts as well as the external forces.

### 3.3 Links, Frames and Kinematic Chains

A link is defined as a rigid body having two or more pairing elements which connect it to other bodies for the purpose of transmitting force or motion (Ham et al. 58).

In every machine, at least one link either occupies a fixed position relative to the earth or carries the machine as a whole along with it during motion. This link is the frame of the machine and is called the fixed link.

The combination of links and pairs without a fixed link is not a mechanism but a kinematic chain.

### 3.4 Skeleton Outline

#### Figure 3-1 Skeleton outline

For the purpose of kinematic analysis, a mechanism may be represented in an abbreviated, or skeleton, form called the skeleton outline of the mechanism. The skeleton outline gives all the geometrical information necessary for determining the relative motions of the links. In Figure 3-1, the skeleton outline has been drawn for the engine shown in Figure 2-1. This skeleton contains all necessary information to determine the relative motions of the main links, namely, the length AB of the crank; the length BC of the connecting rod; A the location of the axis of the main bearing; and the path AC of point C, which represents the wrist-pin axis.

### 3.5 Pairs, Higher Pairs, Lower Pairs and Linkages

A pair is a joint between the surfaces of two rigid bodies that keeps them in contact and relatively movable. For example, in Figure 3-2, a door jointed to the frame with hinges makes revolute joint (pin joint), allowing the door to be turned around its axis. Figure 3-2b and c show skeletons of a revolute joint. Figure 3-2b is used when both links joined by the pair can turn. Figure 3-2c is used when one of the link jointed by the pair is the frame.

#### Figure 3-2 Revolute pair

In Figure 3-3a a sash window can be translated relative to the sash. This kind of relative motion is called a prismatic pair. Its skeleton outlines are shown in b, c and d. c and d are used when one of the links is the frame.

#### Figure 3-3 Prismatic pair

Generally, there are two kinds of pairs in mechanisms, lower pairs and higher pairs. What differentiates them is the type of contact between the two bodies of the pair. Surface-contact pairs are called lower pairs. In planar (2D) mechanisms, there are two subcategories of lower pairs -- revolute pairs and prismatic pairs, as shown in Figures 3-2 and 3-3, respectively. Point-, line-, or curve-contact pairs are called higher pairs. Figure 3-4 shows some examples of higher pairs Mechanisms composed of rigid bodies and lower pairs are called linkages.

### 3.6 Kinematic Analysis and Synthesis

In kinematic analysis, a particular given mechanism is investigated based on the mechanism geometry plus other known characteristics (such as input angular velocity, angular acceleration, etc.). Kinematic synthesis, on the other hand, is the process of designing a mechanism to accomplish a desired task. Here, both choosing the types as well as the dimensions of the new mechanism can be part of kinematic synthesis. (Sandor & Erdman 84)

1 Introduction to Mechanisms
2 Mechanisms and Simple Machines
3 More on Machines and Mechanisms
3.1 Planar and Spatial Mechanisms
3.2 Kinematics and Dynamics of Mechanisms
3.3 Links, Frames and Kinematic Chains
3.4 Skeleton Outline
3.5 Pairs, Higher Pairs, Lower Pairs and Linkages
3.6 Kinematic Analysis and Synthesis
4 Basic Kinematics of Constrained Rigid Bodies