M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Introduction to the study of mechanisms of linked bars

Dynamics

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Types of movement of a rigid body

The movement that we will study will be on the plane so there are three types of movement:

• Pure rotation: The body possesses one point (center of rotation) that has no motion with respect to the stationary frame of reference. All other points on the body describe arcs about that center. A reference line drawn on the body through the center changes only its angular orientation.

Basic concepts

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

• Pure translation: All points on the body describe parallel (curvilinear or rectilinear) paths. a reference line drawn on the body changes its linear position but does not changes its angular orientation.

• Complex movement: a simultaneous combination of rotation and translation. Any reference line drawn on the body will change both its linear position and its angular orientation.

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

DOF or degrees of freedom of a mechanical system:

The number of inputs that need to be provided in order to create a predictable output.

Link

(Hypothetically) is a rigid body which has at least two nodes, which are the points of union with other links.

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

Classification of links

According to the number of nodes: can be binary (with two nodes), ternary (of three nodes) and Quaternary (of four nodes). Its shape can be anyone.

According to the movement: fixed, crank, coupler and slider.

According to function: fixed, driver, transducer and driven.

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

Joint

It is a connection between two or more links (in its nodes), which allows for some movement or potential movement between the connected parts. The joints are also known as kinematic pairs. They are 1 DOF.

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts Kinematic chain

An assemblage of links and joints, interconnected in a way to provide a controller output motion in response to a supplied input motion.

Mechanism

A kinematic chain in which at least one links has been grounded or attached, to the frame of reference.

Machine

A combination of resistant bodies arranged to complete the mechanical forces of nature to do work accompanied by determinate motions.

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

kinematics fixing

It is defined as any link or links that are subject in the space (no movement) in relation to the frame of reference. Also note that the framework itself can, in fact, be moving.

Kinematics inversion

It is created by attaching a different link in the kinematic chain. Therefore, there are so many investments of a Kinematic chain (mechanism) given as links have.

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts DOF or Degrees of freedom to a mechanism:

Also known as "M" mobility and they are the number of entries you need to provide in order to create a predictable output.

• If the GDL are positive we will have a mechanism and the links will be relative motion.

• If the GDL are equal to zero we will have a structure and movement will not be possible.

• If the GDL are negative we have a preloaded structure, which means that any movement will not be possible and some efforts may also be present at the time of Assembly.

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts Gruebler equation for flat mechanisms

Kutzbach equation for flat mechanisms

JLGDLM 2)1(3

212)1(3 JJLGDLM

Multiple joint: The complete number is equal to the number of links that are connected through the multiple link less one. Is it a node is connected 3 links we have a double joint (3-1=2).

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

Semi-joint

Together with 2 DOF that allows two forms of movement.

For example rolls and sliders.

Kinematic diagram

Graphic representation of a body in repeating or oscillating motion in order to facilitate the determination of position, velocity and acceleration in any element of the system given at any instant of time.

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

Mechanism Kinematic diagram

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

Mechanism Kinematic diagram

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

Mechanism Kinematic diagram

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

Parts of a kinematic diagram :

Crank: Link capable of make one complete revolution and this pivoted to the ground. It has angular velocity and in some cases angular acceleration (represents a rigid body in pure rotation and is considered as the input element of the mechanism, where will connect the motor).

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

• Rocker: Also known as oscillator. It has angular velocity and angular acceleration (represents a rigid body in pure rotation and is considered as the output of the mechanism). Its not capable of make a complete revolution (Only oscillate)

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

Coupler: Also known as connecting rod. A link that has complex motion and is not pivoted to a fixed ground element. It has angular velocity and angular acceleration (represents a rigid body in complex motion and is considered the element that communicate the input element with the output element.

M.A Jorge Alejandro Cúpich Guerrero, Dynamics

Basic concepts

• Slider: Rigid body that moves rectilinear or curvilinear about a trajectory. It isn´t angular velocity and angular Acceleration (represents a rigid body in translation and is considered as the output in the mechanism).