Month: April 2016

Brittleness

Brittleness

Brittleness          04/23/16

 

An object is considered brittle if it breaks from stress without significant deformation. Such an object requires little energy to be broken. The brittle strength of an object can be increased by subjecting it to pressure.

Thermoplastics

Thermoplastics

Thermoplastics         

        04/22/16

 

Thermoplastics are plastic materials that become pliable once a certain temperature threshold has been reached and revert back to being rigid once cooled to a certain temperature. The amorphous nature of thermoplastics are less susceptible to chemical attacks and environmental stress cracking due to lacking such a clearly defined structure. Teflon is an example of an application of thermoplastics

Solving first order systems using matrices

Solving first order systems using matrices

      Solving first order systems using matrices               04/21/16

 

Suppose we have a first order system with equations x(t)’ =ax(t)+by(t)and y(t)’=cx(t)+dy(t). We can solve these equation by putting the equations into a matrix form. The matrix will end up with a, b, c, and din progressing order. By taking the determinant, we can find the eigenvalues. We then transform this in to what looks like a solution to a second order differential equation C1*e1t*V1+C2*e2t*V2. We then solve for x(t)and y(t), with the front and bottom rows for the vectors are correlated with the x(t)and y(t)respectfully.

Auxiliary view

Auxiliary view

Auxiliary view                          04/20/16

 

When doing Mechanical Engineering design, many parts often have slanted platforms. These platforms usually become distorted when created using the standard top-front-right views, so Auxillary views were created in response. Auxiliary views take a snapshot of the object from a viewpoint that is centered on the slanted object. This makes it so the object is much easier to visualize. Often, a partial auxillary view is often used so only the important details of the slant are seen (much of the non slanted slide of the part is often unnecessary and becomes distorted itself when viewed through the auxiliary view).

Vector Field Diagrams

Vector Field Diagrams

Vector Field Diagrams          04/19/16

 

A most intuitive way of geometrically representing a solution of equations is through the use of a Vector field Diagram. To construct a vector field diagram, take two sets of equations dxdt=f(x,y)and dydt=g(x,y), set them equal to zero, and then isolate the xand y values on opposite sides. These sets of equations will determine the series of ordered pairs in which the slope is zero (in the horizontal or vertical direction for the f(x,y)and g(x,y) functions respectively). If one wants to see when the values are greater or less than zero, set the functions to a constant c greater than 0, and then solve with yas an isolate. These new solutions will determine the new slope in the x or y directions. One must combine the horizontal and tangential slopes to make the final value

Chain drives vs belts

Chain drives vs belts

Chain drives vs belts           Isaac Gendler

 

One of the most heated decisions a Mechanical Engineer must make is to either utilize a chain drive or a belt for a rotary power transmission system. Chain drives lose much less energy to friction, making them more efficient. Chain drives are also usually stronger, and can slip around geared systems much more smoothly. Chain drives are also usually much narrower, making them easier to wrap around smaller objects. The drawbacks of chain drives is that they often have greater inertia, they can have a non-uniform velocity which can cause entanglement, and can be subject to vibrations.

Chain drive

Chain drive

Chain drive     04/17/16

 

One ingenuitive way that humankind solved the issue of transferring power from one mechanical rounded object to another is through the use of a chain drive. A chain drive used a belt of chain to wrap around a gear  (each teeth is fitted into the holes) and then wrapped around another cylindrical object. Chain drives are often used in transportation applications such as bicycles and automobiles

Representing axises with values

Representing axises with values

Representing axises with values         04/16/16

 

We can Algebraic functions on numerical axises through the use of geometric descriptions. For a linear 1-dimensional axis, we use the variable. For a two dimensional axis, we use and for the First and second dimension respectfully. For a third dimensions, we will add in z, for a 4th we add in w, and when we get to 5 we just convert everything in to roman numerals (becomes I, y becomes II, etc.)

Simple Machines

Simple Machines

Simple Machines      04/15/16

 

Simple machines are devices that change the direction or magnitude of force. In summation, they can be generalized as objects that utilize Mechanical advantage to modify the force values. The six machines identified as simple machines by renaissance scientists include the Lever (a beam fixed on a pendulum or fixed fulcrum), the Wheel and axle (A wheel attached to an axle and allowed to rotate which causes a force transmission), the Inclined plane (A flat planar surface tilted at an angle which is used to lift or lower loads), the wedge (A triangular shaped portable inclined plane), and the Screw (an object that translate rotational motion into linear motion)