Branches of TOM, Machine & Structure, Kinematic Links

Kinematics of Machines (2131906)

PREPARED BY:Vivek Aghara (140030119001)

Akash Ambaliya (140030119003)FX-Division

Introduction

• The subject Theory of Machines may be defined as that branch of Engineering - Science, which deals with the study of relative motion between the various parts of machine, and forces which act on them. The knowledge of this subject is very essential for an engineer in designing the various parts of a machine.

Sub-Divisions of Theory of Machines

• Kinematics It is that branch of Theory of Machines which deals with the relative motion betwen the various parts of the machines with out forces applying to it.

• DynamicsIt is that branch of Theory of Machines which deals with the forces and their effects, while acting upon the machine parts in motion.

Sub-Divisions of Theory of Machines

• KineticsIt is that branch of Theory of Machines which deals with the inertia forces which arise from the combined effect of the mass and motion of the machine parts.

• StaticsIt is that branch of Theory of Machines which deals with the forces and their effects while the machine parts are at rest. The mass of the parts is assumed to be negligible.

Kinematics of machines• The dynamic analysis of a machine requires the

determination of the movement, or kinematics, of its component parts, known as kinematic analysis.

• The assumption that the system is an assembly of rigid components allows rotational and translational movement to be modelled mathematically as Euclidean, or rigid, transformations.

• This allows the position, velocity and acceleration of all points in a component to be determined from these properties for a reference point, and the angular position, angular velocity and angular acceleration of the component.

Machines

• A machine is a tool containing one or more parts that uses energy to perform an intended action.

• Machines are usually powered by mechanical, chemical, thermal, or electrical means, and are often motorized.

Machines

• Machines are assembled from standardized types of components.

• These elements consist of mechanisms that control movement in various ways such as gear trains, transistor switches, belt or chain drives, linkages, cam and follower systems, brakes and clutches, and structural components such as frame members and fasteners.

Mechanisms

• Assemblies within a machine that control movement are often called "mechanisms.“

• Mechanisms are generally classified as gears and gear trains, cam and follower mechanisms, and linkages, though there are other special mechanisms such as clamping linkages, indexing mechanisms and friction devices such as brakes and clutches.

Structures

• If one of the link of a redundant chain is fixed. It is known as structure or locked system.

• The degree of freedom of a structure is 0.

• A structure with a negative degree of freedom is known as superstructure.

Mobility of Mechanisms• The configuration of a system of rigid links connected by

ideal joints is defined by a set of configuration parameters, such as the angles around a revolute joint and the slides along prismatic joints measured between adjacent links.

• The geometric constraints of the linkage allow calculation of all of the configuration parameters in terms of a minimum set, which are the input parameters.

• The number of input parameters is called the mobility, or degree of freedom, of the linkage system.

Mobility of Mechanisms• Joints that connect bodies in this system remove degrees of

freedom and reduce mobility.

• Specifically, hinges and sliders each impose five constraints and therefore remove five degrees of freedom.

• It is convenient to define the number of constraints c that a joint imposes in terms of the joint's freedom f, where c=6-f. In the case of a hinge or slider, which are one degree of freedom joints, we have f=1 and therefore c=6-1=5.

• Thus, the mobility of a linkage system formed from n moving links and j joints each with fi, i=1, ..., j, degrees of freedom can be computed as, Kutzbach-Gruebler's equation

Mobility of Mechanisms

• There are two important special cases: (i) a simple open chain, and (ii) a simple closed chain. A simple open chain consists of n moving links connected end to end by j joints, with one end connected to a ground link. Thus, in this case N=j+1 and the mobility of the chain is

Mobility of Mechanisms

• For a simple closed chain, n moving links are connected end-to-end by n+1 joints such that the two ends are connected to the ground link forming a loop. In this case, we have N=j and the mobility of the chain is

Kinematic Link• Each part of a machine, that undergoes relative

motion with respect to some other part, is called kinematic link (or kinematic element). 

• Kinematic links help in the transmission of motion, from one machine part to another.

• The connecting rods shown in the image below (brown in colour) are individual kinematic links.

• They are used for transmitting motion from piston to crankshaft in an engine.

Types of Kinematic links

• Based on rigidity, kinematic links can be broadly classified into three types.– Rigid link– Flexible link– Fluid link

Rigid Link• Rigid links are those kinematic links that do not

undergo any change of shape when transmitting motion (or when subjected to external forces).

• In reality, no rigid links exist.

• However, kinematic links whose deformation is very small are considered as rigid links.

• Some good examples of rigid links are crankshafts, connecting rods and cam followers.

Flexible link

• A flexible link is a resistant kinematic link that undergoes partial deformation when transmitting motion.

• Its deformation does not hinder its effectiveness of transmission.

• Some examples of flexible links are belts (in belt drives) and chains (in chain drives).

Fluid link• A fluid link makes use of a fluid (liquid or gas) to transmit motion,

by means of pressure.

• Fluid links always undergo deformation when transmitting motion.

• Some good examples where fluid links are used are pneumatic punching presses, hydraulic jacks and hydraulic brakes.

Thank You…