Posts Tagged ‘distance’

Vectors, Sin(ϴ), and the Torque Formula

Wednesday, March 26th, 2014

      Last time we introduced a physics concept known as torque and how it, together with modified gear ratios, can produce a mechanical advantage in devices whose motors utilize gear trains.   Now we’ll familiarize ourselves with torque’s mathematical formula, which involves some terminology, symbols, and concepts which you may not be familiar with, among them, vectors, and sin(ϴ).

Torque = Distance × Force × sin(ϴ)

      In this formula, Distance and Force are both vectors.   Generally speaking, a vector is a quantity that has both a magnitude — that is, any measured quantity associated with a vector, whether that be measured in pounds or inches or any other unit of measurement — and a direction.  Vectors are typically represented graphically in engineering and physics illustrations by pointing arrows.   The arrows are indicative of the directionality of the magnitudes involved.

      Sin(ϴ), pronounced sine thay-tah, is a function found within a field of mathematics known as trigonometry , which concerns itself with the lengths and angles of triangles.   ϴ, or thay-tah, is a Greek symbol used to represent the angle present between the Force and Distance vectors as they interact to create torque.   The value of sin(ϴ) depends upon the number of degrees in the angle ϴ. Sin(ϴ) can be found by measuring the angle ϴ, entering its value into a scientific calculator, and pressing the Sin button.

      We’ll dive into the math behind the vectors next time, when we return to our wrench and nut example and apply vector force quantities.


Achieving Mechanical Advantage Through Torque

Wednesday, March 19th, 2014

      Last time we saw how gear train ratios allow us to change the speed of the driven gear relative to the driving gear.   Today we’ll extend this concept further and see how gear trains are used to amplify the mechanical power output of small motors and in so doing create a mechanical advantage, an advantage made possible through the physics of torque.

      Below is an ordinary electric drill.   Let’s see what’s inside its shell.

Power tool engineering expert witness

      There’s a whole lot of mechanical advantage at work here, giving the drill’s small motor the ability to perform big jobs.   A motor and gear train are housed within the drill itself.   The motor shaft is coupled to the chuck shaft via the gear train, and by extension, the drill bit.   A chuck holds the drill bit in place.

      It’s the drill’s gear train that provides the small motor with the mechanical advantage necessary for this hand-held power tool to perform the big job of cutting through a thick steel plate.   If the gear train and its properly engineered gear ratio weren’t in place and the chuck’s shaft was connected directly to the motor shaft, the motor would be overwhelmed and would stall or become damaged.   Either way, the work won’t get done.

      To understand how operations like these can be performed, we must first familiarize ourselves with the physics concept of torque.   Torque allows us to analyze the rotational forces acting upon rotating objects, such as gears in a gear train and wrenches on nuts and bolts.   Manipulating torque allows us to achieve a physical advantage when rotating objects around a pivot point.   Let’s illustrate this by using a wrench to turn a nut.

mechanical engineering expert witness

      The nut is fastened to the bolt with threads, interconnecting spiral grooves formed on both the inside of the nut and the outside of the bolt.   A wrench is used to loosen and tighten the nut by rotating it on its mating threads.   The nut itself rotates about a pivot point which lies at its center.

mechanical fastener expert

      When you use your arm to manipulate the wrench you apply force, a force which is transmitted at a distance from the pivot point.   This in turn creates a torque on the nut.   In other words, torque is a function of the force acting upon the handle relative to its distance from the pivot point at the center of the nut.

      Torque can be increased by changing one or both of its acting factors, force and distance.   We’ll see how next time when we examine the formula for torque and manipulate it so that a weak arm can loosen even the tightest nut.


Machine Safety, Operator Safety, And Keeping Those Fingers

Sunday, September 27th, 2009

     Crushed fingers, amputations, burns, blindness, these are all too common undesirable occurrences involving moving machinery.  Eliminating the risk of such accidents is an integral part of the engineering design process, where risk assessment goes hand and hand with industry standards in order to provide adequate machine safeguards and protection to operators as well as bystanders.

     Machine safeguards fall into three basic categories: Guards, Devices, and Distance.

     Guards are physical barriers that are added to machines with the goal of keeping body parts, clothing, etc., separated from potentially hazardous areas.  An example would be a metal cage surrounding drive belts and pulleys.  Guards can also serve to keep material fragments and debris from flying out of machines while in operation, such as when an enclosure is built around the grinding wheel of a bench grinder.

     Devices can consist of automatic controllers, often connected to sensors on machine componets.  These controllers use a form of “safety interlock logic” to monitor the operating state of machinery.  They must act quickly and automatically to stop the normal operation of a machine if they sense that an undesirable object, say a person’s forearm, is in danger of entering a hazardous area.

     Controllers can be in the form of hard-wired electromechanical relays, embedded microprocessors, or programmable logic controllers (PLCs).  Their sensors can include electrical switches embedded in floor mats or mounted on movable guards, incorporated into control handle grips, or linked to an access door latch.  Still other sensors are more elaborate, using more sophisticated methods to maintain safety, such as photoelectric devices known as laser curtains.  These act by spreading beams of light across an opening which may be a gateway to a dangerous area.  If the beam is broken by an object, the controller takes appropriate action and renders the machinery inoperable.

     Distance safeguards operate as you would infer them to, by designing machinery so that hazardous areas are kept a great enough distance from body parts, etc., so as to eliminate any danger of them being drawn into an unsafe area.  An example of this factor at work would be when machinery is developed so that moving gears and other potential hazards are kept far out of the reach of someone by virtue of their overall design. 

      Sometimes even the best machine safeguard designs can be rendered ineffective after a piece of machinery is put into actual operation.  The reasons for this are varied, from poor maintenance of equipment, to lack of training for operating personnel, to inadequate supervision of workers, or perhaps the machine has been modified to operate outside the parameters of its design capacity.  Whatever the reason, people can be put at risk for serious injury and even death if machine safeguards are bypassed, eliminated, and defeated.