Notes on kinematics pdf

Co-planar vectors- Vectors situated in one plane, irrespective of their directions, are known as co-planar vectors. Vector addition Vector addition is commutative-. Vector addition is associative-.

Vector addition is distributive-. Magnitude of resultant vector Unit Vector:- Unit vector of any vector is a vector having a unit magnitude, drawn in the direction of the given vector. In three dimension,. Area of triangle Area of parallelogram Volume of parallelepiped Equation of Motion in an Inclined Plane:. Here, V B is called reference object velocity.

Here, m 0 is the rest mass of the body, v is the speed of the body and c is the speed of light. Please choose valid name. Please Enter the valid Email.

Select Grade 6th 7th 8th 9th 10th 11th 12th 12th Pass Please choose the valid grade. We receieved your request Stay Tuned as we are going to contact you within 1 Hour Close. Thank you for registering. One of our academic counsellors will contact you within 1 working day.

Please check your email for login details. Studying in Grade 6th to 12th? Registration done! Sit and relax as our customer representative will contact you within 1 business day Continue.

Book a free demo of live class. Revision Notes on Kinematics Inertial frame of reference:- Reference frame in which Newtonian mechanics holds are called inertial reference frames or inertial frames. Reference frame in which Newtonian mechanics does not hold are called non-inertial reference frames or non-inertial frames.

The average speed v av and average velocity of a body during a time interval? Average acceleration is defined as the change in velocity over a time interval? The three equations of motion for an object with constant acceleration are given below. Displacement x Velocity v Acceleration a a At rest b Motion with constant velocity c Motion with constant acceleration d Motion with constant deceleration Scalar Quantities:- Scalar quantities are those quantities which require only magnitude for their complete specification.

Sandeep Bhaskar. A short summary of this paper. Lecture notes on Kinematics Dr. Design process means the synthesis during the proposal phase the size, shape, material properties and arrangements of the parts are prescribed in order to fulfil the required task. Analysis is a technique or rather set of tools allowing critical evaluation of existing or proposed design in order to judge its suitability for the task. Thus synthesis is a goal that can be reached via analysis.

Mechanical engineer deals with many different tasks that are in conjunction to diverse working processes referred to as a technological process. Technological processes involve transportation of material, generation and transformation of energy, transportation of information. All these processes require mechanical motion, which is carried out by machines. Thus the mechanics as a science is involved in the design process. Mechanics represents the science that includes Statics, Dynamics, and Mechanics of Materials.

Statics provides analysis of stationary systems while Dynamics deals with systems that change with time and as Euler suggested the investigation of motion of a rigid body may be separated into two parts, the geometrical part and the mechanical part. Within the geometrical part Kinematics the transference of the body from one position to the other is investigated without respect to the causes of the motion. The change is represented by analytical formulae. Thus Kinematics is a study of motion apart from the forces producing the motion that is described by position, displacement, rotation, speed, velocity, and acceleration.

In Kinematics we assume that all bodies under the investigation are rigid bodies thus their deformation is negligible, and does not play important role, and the only change that is considered in this case is the change in the position. Terminology that we use has a precise meaning as all the words we use to express ourselves while communicating with each other.

It is useful to clarify certain terms especially in areas where the terminology is not very clear. Structure represents the combination of rigid bodies connected together by joints with intention to be rigid. Therefore the structure does not do work or transforms the motion.

Structure can be moved from place to place but it does not have an internal mobility no relative motion between its members. Machine — device used to alter, transmit, and direct forces to accomplish a specific objective.

Mechanism — the mechanical portion of a machine that has the function of transferring motion and forces from power source to an output.

Mechanism transmits motion from drive or input link to the follower or the output link. The motion is limited to two-dimensional space and behaviour of all particles can be observed in true size and shape from a single direction.

Therefore all motions can be interpreted graphically. Most mechanisms today are planar mechanism so we focus on them. Spherical mechanism — each link has a stationary point as the linkage moves and the stationary points of all links lie at a common location.

Thus each point draws a curve on the spherical surface and all spherical surfaces are concentric. Spatial mechanism — has no restriction on the relative motion of the particles. Each mechanism containing kinematical screw pair is a spatial mechanism because the relative motion of the screw pair is helical.

The mechanism usually consists of: Frame — typically a part that exhibits no motion Links — the individual parts of the mechanism creating the rigid connection between two or more elements of different kinematic pair. Springs cannot be considered as links since they are elastic. Kinematic pair KP represents the joint between links that controls the relative motion by means of mating surface thus some motions are restricted while others are allowed.

The number of allowed motions is described via mobility of the KP. The mating surfaces are assumed to have a perfect geometry and between mating surfaces there is no clearance. Joint — movable connection between links called as well kinematic pair pin, sliding joint, cam joint that imposes constrains on the motion Kinematic chain is formed from several links movably connected together by joints.

The kinematic chain can be closed or opened according to organization of the connected links. Our computation of the forces was based on the Statics only and at the beginning we assumed that the forces exist on the structure or are applied very slowly so they do not cause any dynamical effect on the structure.

This situation is far from real world since there is nothing stationary in the world. It is a study of the geometry of motion that involves determination of position, displacement, speed, velocity, and acceleration. This investigation is done without consideration of force system acting on an actuator.

Actuator is a mechanical device for moving or controlling a mechanism or system. Therefore the basic quantities in Kinematics are space and time as defined in Statics.

The motion is described by three kinematics quantities: The position vector gives the position of a particular point in the space at the instant. The time rate of change of the position vector describes the velocity of the point. Acceleration — the time rate of change of the velocity All quantities — position, velocity, and acceleration are vectors that can be characterized with respect to: Change of a scalar magnitude — uniform motion Uniformly accelerated motion Non-uniformly accelerated motion Harmonic motion Character of the trajectory - 3D motion in the space 2D planar motion The type of trajectory can be specified as: Rectilinear motion Rotation Universal planar motion Spherical motion Universal space motion Complex motion The set of independent coordinates in the space describes the position of a body as a time- function thus defines the motion of a body.

The number of independent coordinates corresponds to the degree of freedom of the object or set of coupled bodies and it is expressed as the mobility of the object. Mobility — the number of degrees of freedom possessed by the mechanism.

The particle can have a mass associated with that does not play role in kinematical analysis. Consider an unconstrained body in the space How many points will describe position of a body? To be able to evaluate DOF the kinematical diagram of the mechanism has to be created. Diagrams should be drawn to scale proportional to the actual mechanism in the given position. The convention is to number links starting with the reference frame as number one while the joints should be lettered.

The adopted strategy should consist of identifying on the real set of bodies: the frame, the actuator, and all the other links all joints any points of interest and draw the kinematical diagram according to the convention.

Once we evaluated the mobility degrees of freedom we can identify the corresponding set of independent coordinates parameters and start the kinematical analysis of the mechanism 7 Dr. The time limit for computation of the instant velocity is approaching zero. A common sense or rather to say intuition suggests that the velocity has the tangent direction to the trajectory.

To derive the expression for acceleration we need to draw velocity vector diagram so called velocity hodograph. The end points of their vectors are creating the desired curve hodograph. The tangent component of acceleration captures the change of magnitude of a velocity while the normal component captures the change of direction of a velocity.

The positional vector form will vary according to the type of the coordinate system. This process is called Orthogonal Transformation of Vector Quantities 2. The moving point A is connected to the CS2, which moves with respect to the reference frame.

The task is to project vector r2A into CS1.