Introduction to Robotics

Introduction to Robotics
Part 3: Propulsion System Robotics and Automation Also called the motion system Copyright © Texas Education Agency, All rights reserved.

Copyright © Texas Education Agency, 2012. All rights reserved.
Robot Systems Structural System Physical system that provides support and stability Propulsion System (motion) Drive system includes motors, wheels, and gears Control System Microcontroller, operating program, electrical power, and joystick Tool and Actuator system Arms, grippers, manipulators Sensor and Feedback system Perception, transducers There are different ways of describing robot systems, these are sometimes called subsystems. There are often more systems described than these (examples: sensors often have their own system, programming is often considered separately, other systems include power and logic which are included here in the control system). Each of these systems work together, there will be some functional overlap. You can also separate by pure electronic parts vs. electromechanical parts. The actuator and feedback system is how the robot completes the performance objectives. Sensor and manipulation system. The control system is for the internal robot environment, the sense and manipulation system is for the external environment. Copyright © Texas Education Agency, All rights reserved.

Propulsion System Components
Also called the motion system The most important propulsion system components are gears and motors. All examples shown are for permanent magnet type DC motors. We will discuss servos in another section because they are used primarily in arms, actuators, and grippers. Copyright © Texas Education Agency, All rights reserved.

Gears Gears are used for several things: To increase the speed of rotation To increase the torque, or the rotating force applied to a load To change the direction of a torque Gears trade one for the other: If you use gears to increase speed, torque will decrease. If you use gears to increase torque, speed will decrease. Or (with a rack and pinion gear) to change rotary motion into linear motion. This is not designed to be a complete tutorial on gears, only to introduce some basic concepts. There are many good sources of information gears and how they are used on internet websites. Teachers are encouraged to research some in preparation for this lesson. Copyright © Texas Education Agency, All rights reserved.

More Gear Info Gears use teeth to transmit torque. Teeth must be the same size, even on different size gears. The number of teeth varies for different size gears: A smaller gear has fewer teeth A larger gear has more teeth A big gear driving a small gear increases speed. A small gear driving a big gear increases torque. Gear tooth size is called the pitch, and has to be the same if you want gears to work together. Different size means different radius or number of teeth. Teachers may want to locate animation of gears on the internet to show students. Copyright © Texas Education Agency, All rights reserved.

Gear Calculations The ratio of the number of gear teeth equals the ratio of the torque. { Assume gear one (g1) driving gear two (g2) } 𝑔 1 𝑔 2 = 𝑇 1 𝑇 2 The ratio of gear teeth equals the inverse ratio of the speed. 𝑔 1 𝑔 2 = 𝑆 2 𝑆 1 Gear 1 is called the driving gear, gear 2 is called the driven gear (or the follower). These formulas come from conservation of energy (work), F1d1=F2d2 Copyright © Texas Education Agency, All rights reserved.

Optimal Gear Ratio There is an optimal gear ratio. The optimal gear ratio puts load torque on the motor at exactly half stall torque. Load torque on the motor is due to: The weight of the robot The number of drive wheels (motors used) The diameter of the drive wheels This gear ratio will maximize robot speed and motor efficiency. We will have to fully understand how a DC motor works in order to determine the optimal gear ratio. Copyright © Texas Education Agency, All rights reserved.

Motors A motor converts electrical energy into mechanical energy. The mechanical energy comes from the interaction between two magnetic fields. Magnetic fields produce physical forces: Like poles repel (N – N, S – S) Unlike poles attract These forces make a motor spin. One magnetic field is usually a permanent magnet, the other is an electromagnet. Smaller, hobby type motors (like those used in student robots) use permanent magnets because they produce a lot of magnetic field strength for their size and are relatively cheap. Larger motors use wound coil electromagnets in their field windings. The electromagnet allows us to vary the field strength by increasing or decreasing the supply voltage. Copyright © Texas Education Agency, All rights reserved.

Types of Motors Most motors are 2 wire, but some hobby motors are 3 wire because they are modified servos. 2 wire motor may require a motor driver board to provide higher current. 3 wire motors use a servo type RC signal output and are generally low current. Photo Credit: VEX Robotics, Inc. Students sometimes get modified servos that act like motors and real servos mixed up because they look the same. However, they will not work the same. A servo connected to where a motor should go will not work right. Make sure students look at the label before they physically mount these! Students also need to know that these items cost money because they can be burned up or broken. Copyright © Texas Education Agency, All rights reserved.

Example Motor Specs Free Speed: 100 rpm Stall Torque: 8.6 in-lbs Stall Current: 2.6A Free Current: 0.18A All motor specifications are at 7.2 volts. Often designed to connect to a specific structural system: Drive shaft connection Mounting connections Example motor specs. The higher the load on the motor (higher robot weight for example), the slower the speed and the more current it will draw. Stall current is when the shaft binds and is not allowed to spin at all. Current and power ratings are for continuous power without overheating. Heat damage is due to insulation breakdown, mechanical damage is due to centrifugal forces. Photo Credit: VEX Robotics, Inc. Note screw connections sizes such as 6-32 or 8-32 Copyright © Texas Education Agency, All rights reserved.

DC Motor Speed A DC motor is a variable speed device. Speed is controlled by the amount of DC voltage applied: Varying the amount of DC voltage is covered under control systems The physical load applied to the motor also affects its speed: A higher load slows it down There are constant speed motors but we do not cover them here. A larger load will make all types of motors draw more current. We do not say the load controls the speed, the speed changes are an effect of the load. Copyright © Texas Education Agency, All rights reserved.

Motor Specs One interesting note is that as the load on a DC motor increases, it will draw more current from the power supply and make the motor rotate more slowly. DC motor speed is inversely related to motor current (but proportional to voltage). The torque a motor provides is always equal to its load. We will discuss this in more detail later. The higher the load on the motor (higher robot weight for example), the slower the speed of rotation and the more current it will draw. This seems to be counterintuitive (and violate Ohms Law) but it does not because the supply voltage gets split between field winding current and CEMF, not all of the voltage is used to increase magnetic field strength. We will describe the reason (CEMF) a little later. Stall current is when the shaft binds and is not allowed to spin at all, and this produces maximum current and torque. Copyright © Texas Education Agency, All rights reserved.

Motor Specs Motors turn and spin, so we have to start thinking about rotating motion. Many motor formulas and equations involve rotational units and concepts. Angular velocity is the primary term used in rotational motion. Greek symbols are used for the quantities. W w ω is the lowercase Greek symbol omega. The uppercase Greek symbol for omega is the familiar Ω , the symbol for the unit Ohm in Ohm’s Law. Copyright © Texas Education Agency, All rights reserved.

Angular Velocity Angular velocity has a symbol, ω (omega) The speed that something is rotating In America we use RPM, or rotations per minute Science uses units of radians per second There are 60 seconds per minute and 2π radians per rotation, so: 60 RPM = 2π 𝑟𝑎𝑑 𝑠𝑒𝑐 Copyright © Texas Education Agency, All rights reserved.

Conversion Practice Convert 150 RPM to 𝑟𝑎𝑑 𝑠𝑒𝑐 Convert 12π 𝑟𝑎𝑑 𝑠𝑒𝑐 to RPM Convert 85 𝑟𝑎𝑑 𝑠𝑒𝑐 to RPM A motor rotates 120 times in 200 min. Convert this speed to 𝑟𝑎𝑑 𝑠𝑒𝑐 . A motor rotates 1 radian in 2.5 sec. Convert this speed to RPM. These are examples, you can easily make you own examples. Copyright © Texas Education Agency, All rights reserved.

DC Motors A motor has several parts: The rotor (the spinning part) Connected to an axle which is also the rotor shaft The stator (stationary part) The frame Supports the permanent magnets The commutator Switches the DC voltage polarity for continuous rotation (polarity has to switch every half rotation) The brushes Gets electricity into the rotor You may want to search the internet for good quality cutaway diagrams of brushed DC motors. The rotor shaft couples the motor to the external load. Copyright © Texas Education Agency, All rights reserved.

Permanent Magnet DC Motor
This is an old motor that has water damage and is no longer working. It’s only useful purpose is for demonstration. Copyright © Texas Education Agency, All rights reserved.

Bearings The commutator connects to the field windings. The commutator has many segments to provide power to the many armature field coil windings. The commutator segments also prevent the positive and negative power supply voltage from shorting due to the fact that the brushes connect to more than one commutator segment as the rotor spins. Commutator Armature Copyright © Texas Education Agency, All rights reserved.

Permanent Magnet Field Poles Brushes The brushes are stationary and provide an electrical connection to the spinning armature electromagnetic field windings through the commutator. There are springs inside the brush housing that hold the brush against the commutator. The positive and negative DC voltage on these wires connects to the brushes giving power to the armature field. Copyright © Texas Education Agency, All rights reserved.

Brief Motor Description
An increase in motor load requires the motor to draw more current from the power supply. An increase in load slows the motor down, and the decrease in speed decreases something called CEMF, allowing the current to increase, creating higher motor torque which balances the increase in load. Current is directly related to motor torque because torque is produced through the interaction of 2 magnetic fields. Magnetic field strength increases with current. CEMF is Counter Electro Motive Force, also called back emf. The higher the load on the motor (higher robot weight for example), the slower the speed of a motor and the more current it will draw. Stall current is when the shaft binds and is not allowed to spin at all. We will describe CEMF a little later. Copyright © Texas Education Agency, All rights reserved.

Generator Action In order to understand how a motor works, you must understand how a generator works. A generator converts mechanical energy into electrical energy. The mechanical energy comes from an external source called a prime mover. The electrical energy is created from a conductor moving relative to a magnetic field: Relative motion. The principle for electrical generation is called Faraday’s Law. Three things are necessary for electricity generation (also called induction): a conductor, a magnetic field, and relative motion between the two. The mechanical energy is an input and is what creates the motion. In a generator, the conductor is moved due to the input mechanical energy. There is another device called a transformer that creates induction when the magnetic field moves past a stationary conductor. The movement of the magnetic field in a transformer is caused by alternating current expanding and collapsing a magnetic field around a coil. Copyright © Texas Education Agency, All rights reserved.

Motor Action in a Generator
Current in a conductor creates a magnetic field. The magnetic field created by the induced current always opposes the original field. The interaction of the 2 fields creates a force that opposes the applied mechanical force. This is the load on a generator. More current drawn creates a larger mechanical force which opposes the applied mechanical force from the prime mover. More current out of a generator places more of a mechanical load on the generator which has to be overcome by the applied, input mechanical energy. In no case do you get something from nothing, so in both a motor and a generator the production of energy produces a load that opposes the applied energy. Copyright © Texas Education Agency, All rights reserved.

Generator Action in a Motor
A motor also has induction due to conductors moving in a magnetic field. The induced voltage always opposes the applied voltage from the power supply. The induced voltage in a motor is called CEMF. A larger external load slows the motor down, it produces less CEMF and draws more current from the power supply. Counter Electro Motive Force, also called back emf. CEMF is proportional to speed. In an earlier slide we discussed how an increased load on a motor slows it down, reducing the CEMF, forcing it to draw more current from the power supply. Supply voltage is spit between 2 things, CEMF and voltage to the field windings, so as CEMF goes down more voltage is given to the field windings increasing current and magnetic field strength. The current is the power input to a motor, a larger load logically requires more power in. A lower external load allows the motor to speed up. Higher motor speed creates higher CEMF and the motor will draw less current from the external power supply. [Electromotive force] has turned out to be an unfortunate choice of words which is still with us 160 years later. In all of physics except electromagnetic induction, the term 'force' is reserved for mechanical action on physical matter and is measured in units called newtons. In contrast electromotive force is measured in units of volts and causes charge separation. The two types of forces also differ dimensionally and in the distances over which they work. EMF also does not feel the equal and opposite force of newtons third law. Furthermore, EMF does not follow the inverse square law but is only inversely proportional with distance. Copyright © Texas Education Agency, All rights reserved.

Motors and Generators Motors convert electrical energy into mechanical energy. Generators convert mechanical energy into electrical energy. All motors are generators and all generators are motors. The load on a generator is the physical force created by the interaction of 2 magnetic fields. The electrical load on a motor is the current which is controlled by the induced voltage due to conductors moving in a magnetic field. When a motor starts to spin, all of the conditions needed for electrical generation are present. The generated electricity opposes the applied electrical energy, the difference is always the mechanical energy out which equals the load. In a generator, the produced electricity creates a mechanical load that opposes the mechanical input energy. Look at each from the standpoint of the external load determines the demand on both, and as the external load increases more input is needed. Copyright © Texas Education Agency, All rights reserved.

Motor Characteristic Curves
All motor specifications are at 7.2 volts This is for a geared motor, typical for one found in a student robot. This shows the relationship between motor torque, motor speed, and motor current. Torque is the common axis, and represents the load. As load goes up, motor current goes up and motor speed goes down. A vertical line going up from the torque (which is a function of the load applied to the motor) will cross both the speed and current lines, where the vertical torque line crosses each will be the respective speed and current for the motor at that load. Example: at 7.5 N-cm, speed is about 30 RPM and current is about 1.6 amps. The actual current and speed can be calculated for a given motor. To re-phrase: students will calculate current and speed values for a given load on a given motor. In fact, the primary purpose of this module is to demonstrate the importance of math to robotics and technology. Copyright © Texas Education Agency, All rights reserved.

Motor Current and Torque
This line shows that current and torque are directly proportional Torque (N-cm) 150 100 50 Speed (RPM) Current (amps) .4 .8 2.0 1.2 1.6 5.0 2.5 7.5 10 A larger current increases magnetic field strength, creating increased forces which turn the motor. What is less clear is that the increased current is a result of a larger motor load, not a cause of the higher torque. Current is what the motor has to draw from the power supply, and is a function of speed. Copyright © Texas Education Agency, All rights reserved.

Motor Speed and Torque This line shows that current and speed are inversely proportional, meaning that as torque goes up, speed goes down Torque (N-cm) 150 100 50 Speed (RPM) Current (amps) .4 .8 2.0 1.2 1.6 5.0 2.5 7.5 10 The torque generated is equal to the load applied to the motor, so you can properly say this is speed vs. load. While it is logical that an increased load will slow the motor down, the actual mechanism behind this effect is a little more complicated. Motor torque and load are the same thing. Copyright © Texas Education Agency, All rights reserved.

No-Load Speed ωn Speed and current values for a motor that has no load applied to it, meaning it is free spinning. Current is minimum, speed is maximum. No-Load Current Copyright © Texas Education Agency, All rights reserved.

Stall Current Stall current is also called locked rotor current, and is the current due to winding resistance. There is no CEMF to help limit current when the motor is not turning. Stall Torque τs Copyright © Texas Education Agency, All rights reserved.

Motor Characteristic Formulas
τmotor = τs - τs ω𝑚 ωn = τs (1 - ω𝑚 ωn ) ωmotor = ωn ( 1 - τm τs ) These formulas are related to the curves (plot lines) shown on the previous slides. Given a supply voltage and a load, a student can calculate motor speed. All of the formulas shown are versions of the same formula. These formulas can be converted from one to another (solving for different variables) using algebra. τmotor (τm) and ωmotor (ωm) are actual motor operating torque and speed Copyright © Texas Education Agency, All rights reserved.

The stall torque, τs, represents the point on the graph at which the torque is a maximum, which is when the shaft is not rotating. No rotation means no CEMF which allows maximum current. The no load speed, ωn, is the maximum output speed of the motor (when no load torque is applied to the output shaft meaning the motor is freely spinning). You should go back and forth over the previous slides to relate all these variables. Copyright © Texas Education Agency, All rights reserved.

Torque, Current, and Speed
Torque is proportional to current. Current is proportional to supplied voltage. The relationship between speed and current is more complex. Speed is inversely proportional to current. Torque generated equals the load applied. As load increases, the motor slows down, current increases, torque generated rises to meet the higher load. There is a minimum amount of voltage and current necessary to get the motor to rotate, but a motor will spin at a fairly high speed with no external load. Maximum torque is generated when the motor is not spinning. When it starts spinning a back or counter emf is generated that opposes applied voltage. This counter EMF is a function of motor speed. The faster a motor spins, the more counter emf is generated, the more opposition to applied voltage, the lower the current. Copyright © Texas Education Agency, All rights reserved.

Motor Formulas I = 𝑉𝑆 𝑉𝑒 𝑅 From Ohms Law: Where: VS = Supply voltage (from power supply or control circuit) I = Motor Current (Amps) R = Terminal Resistance (Ohms) Ve = Back EMF (Volts) (also called counter emf, or CEMF) The back EMF generated by the motor is directly proportional to the angular velocity of the motor. V stands for voltage and not velocity. There is a similar formula that relates angular velocity to linear velocity. The back emf (electromotive force) is caused by generator action in the motor, and always opposes the supplied voltage. (Lenz’s Law) 7.2 VDC is a common hobby robot supply voltage because a common RC battery pack is made from 6 batteries. Ve = ke·ω Copyright © Texas Education Agency, All rights reserved.

Formula Application We will only use these simple equations in our calculations. There are actually many other factors that influence motor operation. Fortunately, most of those factors are constant for a given motor and can be accounted for in a single constant of proportionality. See the next slide for an example of some of the factors we will NOT be taking into account These are factors that would help determine the value of the constant of proportionality ke. Copyright © Texas Education Agency, All rights reserved.

Φ = μAI 𝑁 𝑙 Φ = magnetic flux density μ = magnetic permeability of the core A = cross sectional are of the magnetic pole I = current N = number of turns of wire around the core l = path length of the flux field This is included for information only. Other factors include the size of the wires, the magnetic air gap between rotor and stator, the number of magnetic poles, and the construction of the poles. Copyright © Texas Education Agency, All rights reserved.

Additional Formulas Speed equals cemf over shunt field flux N = 𝑉𝑒 Φ Motor Torque equals armature current times shunt field flux τ = Ia · Φ Tangential velocity, v = r·ω Power in rotational motion: P = τ ·ω Copyright © Texas Education Agency, All rights reserved.

Typical Questions Assume you have a particular motor with specs for that motor. What is the constant of proportionality, ke, for that motor? Given a load, what is the motor speed? What current does the motor draw? How does motor speed vary with applied voltage? Copyright © Texas Education Agency, All rights reserved.

Example 1 Use the specs for the motor given on slide 8 Free Speed: 100 rpm Stall Torque: 8.6 in-lbs Stall Current: 2.6A Free Current: 0.18A All motor specifications are at 7.2 volts Calculate ke , speed, and current for this motor given motor load equals 3 in-lbs Copyright © Texas Education Agency, All rights reserved.

Example 1 Calculate R from stall current (ω = 0, Ve = 0) Calculate Ve from free running current Calculate ke from Ve (use free running speed) Ve = ke · ω, ke = 𝑉𝑒 ω = 6.7 𝑉 100 𝑅𝑃𝑀 = 𝑽 𝑹𝑷𝑴 I = 𝑉𝑆 𝑉𝑒 𝑅 Solve for R, R = 𝑉𝑠 𝐼𝑆 = 7.2 𝑉 2.6 𝐴 = 2.77 Ω Ve = VS – IR = 7.2 V – (.18 A · 2.77 Ω) = = 6.7 V R is winding resistance (and is constant for a given motor), ω is angular velocity, and should properly be calculated in radians per second. We used RPM to make it simple, but if you do the conversion 100 RPM equals rad/sec. Once you have Ke you can do all kinds of calculations for a motor. Ke is different for each motor, but is also constant for a given motor. Copyright © Texas Education Agency, All rights reserved.

Example 1 continued Calculate motor speed from load To calculate current, you need Ve ωmotor = ωn ( 1 - τ τs ) = 100 RPM ( 𝑖𝑛−𝑙𝑏𝑠 8.6 𝑖𝑛−𝑙𝑏𝑠 ) = 65.1 RPM Ve = ke · ω = · 65.1 = V I = 𝑉𝑆 𝑉𝑒 𝑅 = 7.2 𝑉 − 4.36 𝑉 2.77 Ω = 1.02 A Copyright © Texas Education Agency, All rights reserved.

Efficiency Motor efficiency is power out divided by power in. Power out is mechanical energy, P = τ · ω Power in is electrical energy, P = V · I % Eff = 𝑃𝑜 𝑃𝑖 x 100 = τ · ω V · I = 𝑁−𝑚 · 6.82 𝑟𝑎𝑑/𝑠𝑒𝑐 7.2 𝑉 ·1.02 𝐴 Units for both need to be the same, so we must convert to metric units. Electrical Power is watts, which is joules per second, so we need angular velocity to be in radians per second. 1 inch-lb = .113 N-m, so 3 in-lb = .339 N-m. ω = 65.1 RPM, 60 RPM = 2π radians/sec, so 65.1 RPM = 6.82 rad/sec. This is basically a unit conversion problem. These values are actual operating values for a real motor as calculated on the previous slides. Make sure you use those calculated values. = 𝑗𝑜𝑢𝑙𝑒𝑠/𝑠𝑒𝑐 𝑗𝑜𝑢𝑙𝑒𝑠/𝑠𝑒𝑐 𝑋 100=31.5% Copyright © Texas Education Agency, All rights reserved.

Robot Linear Speed Assume the motor is coupled directly to a wheel. The formula is slightly different when using American units vs. metric units. American Units: Ѵ = ω · C Metric Units: Ѵ = ω · r V in this case is velocity. American units has velocity in inches per minute (should be converted to feet per minute) while metric units would give a velocity in meters per second. Units for ω in RPM, C is circumference of the wheel = 2πr Units for ω in radians per second, r is radius of the wheel Copyright © Texas Education Agency, All rights reserved.

Calculating Linear Speed
Wheel diameter equals 2.75 inches. Ѵ = ω · C = ω · π d = 65.1 RPM · π · 2.75 in = 𝑖𝑛 𝑚𝑖𝑛 = 𝑓𝑡 𝑚𝑖𝑛 This is NOT the optimal speed of the robot. Optimal speed would require gears that place the load on the motor equal to half of the stall torque. Copyright © Texas Education Agency, All rights reserved.

Optimal Robot Speed The example value of 3 in-lb load on the motor is due to the weight of the robot and the radius of the wheel used. To increase the load on the motor to 4.3 in-lb, use a gear train with a gear ratio of: 4.3 𝑖𝑛−𝑙𝑏 3 𝑖𝑛−𝑙𝑏 = 1.433 Which would increase robot speed to 𝑓𝑡 𝑚𝑖𝑛 Torque equals force times distance. This gear ratio can be given by a gear with 43 teeth driving a gear with 30 teeth. Copyright © Texas Education Agency, All rights reserved.

Robot Weight The example value of 3 in-lb load on the motor is due to the weight of the robot and the radius of the wheel used. The weight of the robot can be calculated: Assuming 2 drive wheels, the actual example robot weight equals 4.4 lb τ = F · r or F = τ 𝑟 = 3 𝑖𝑛−𝑙𝑏 𝑖𝑛 = 2.2 lb Torque equals force times distance. Use this formula with the actual weight of your robot and your wheels to calculate the torque load on your motors, then find the gear ratio needed to optimize speed on your robot. Copyright © Texas Education Agency, All rights reserved.

Additional Examples The following slides show motor specifications for the actual motors used in the BEST robotic contest. Use these specifications for example problems using real world examples. Graphs are included for visual clarity, but students can be expected to create these graphs themselves from information given. Use the example motor specs to have students work problems similar to those worked in this lesson. Instead of giving students this information, you can have them look it up to add even more of a real world simulation. Copyright © Texas Education Agency, All rights reserved.

Motor 2 specs Free Speed: 43 RPM Stall Torque: 24 in-lbs Stall Current: 3.34 amps Free Current: 0.32 amps Use these specs for students to work the same problems demonstrated in the last set of calculations. Price: $44.99 (2.71 N-m) All motor specifications are at 7.2 volts Copyright © Texas Education Agency, All rights reserved.

Example Motor 2 Torque (N-cm) 50 40 10 Speed (RPM) Current (amps) 1.0 4.0 2.0 3.0 100 200 300 30 20 These values are for a med-large geared hobby motor typical for one found in a robot. This is the graph that represents the values from motor 2 specs, an advanced assignment is to have students create this graph from the specs. If so, do not show students this graph. The torque axis is given in metric units, which is a simple conversion from American units. Copyright © Texas Education Agency, All rights reserved.

Motor 3 specs Free Speed: 90 RPM Stall Torque: 8.9 in-lbs Stall Current: 2.39 amps Free Current: 0.21 amps Use these specs for additional student practice. 1 m = inch, 1 inch = m 1 inch-lb = .113 N-m (9.49 = 1.07 N-m, 8.9 = 1.006N-m) All motor specifications are at 7.2 volts Copyright © Texas Education Agency, All rights reserved.

Example Motor 3 2.4 2.0 150 1.6 100 Current (amps) 1.2 Speed (RPM) .8 50 These values are for a med-small geared hobby motor typical for one found in a robot. This is the graph that represents the values from motor 3 specs, an advanced assignment is to have students create this graph from the specs. .4 25 50 75 100 125 Torque (N-cm) Copyright © Texas Education Agency, All rights reserved.

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