inv = tan inv = tan . Many gear-making processes (including hobbing, milling, and shaping) rely on the operator accurately touching-off on the part. The previous section derived the formula for calculating the center distance a of two corrected gears: \begin{align}\label{a}&a = m \cdot( z_1 + z_2) \cdot \frac{\cos(\alpha_0)}{2 \cdot \cos(\alpha_b)} \\[5px]\end{align}. From the list, select Spur Gear. During the touch-off the operator slowly brings the cutting tool into the gear blank until it just begins to touch, then the full depth is dialed in relative to the touch-off. Rack Generation . Pinion cutters, or shapers, are pinion generation tools commonly used in . Notes about browser compatibility: all new major browsers are supported (i didn't tested IE), but unfortunately Chrome can't render SVG circle correctly. Connection angle: Hydraulics Pneumatics With the involute function according to equation (\ref{involute}), the tooth thickness s at an considered circle with the diameter d is completely determined. : a simple tool to make symbol entry easier when typing. 374-376. Update 1.4: TA-DA: Added internal gear support, and the ability of positioning the first gear. : diameter at bottom of root radius of tooth The other angle, SOP^=\hat{SOP} = \varphiSOP^=, can be found following the next steps: The last expression is the involute function. You can input the value of the gear pressure angle \alpha to obtain right away the value of the relative involute function. Hardware, Imperial, Inch Its value remains constant during the operation of the gears; hence it is characteristic of a given design. of an involute gear based on its module, On the other hand, smaller teeth obtained by reducing the pressure angle \alpha give advantages to the smoothness of the operation. A wider tooth is a stronger tooth that can withstand bigger loads. Downloads There are 8 cutters for different teeth cutting requirements. The tip diameters da* correspond to the shortened tip circles, if a tip shortening was carried out. Involute Gear Cutters and Module Gear Cutters - Newman Tools For continuous power transmission, a new tooth must be engaged before the preceding tooth leaves the line of contact. The following online calculator computes the basic dimensions and tooth profile of an involute gear based on its module, number of teeth and pressure angle (the latter is usually 20). The contact ratio must therefore always be greater than one. : hand tools and accessories that I've made. Clocks use the cycloidal or triangular tooth forms. The latter is simply the reference diameter divided by the number of teeth. +, Internal Gear: More here, Use left/right arrows to navigate the slideshow or swipe left/right if using a mobile device. : maximum bearing (or contact) stress on tooth surface How does our involute function calculator work? To select a gear cutter, follow these steps: 1. Enter the precision grades of the two gears as well as absence or existence of tooth form correction (s). More information about this in the privacy policy. : some information about my woodworking workshop. : improvements and tooling for my Harrison M250. The angle in the equations above is to be considered as an auxiliary quantity and generally does not correspond to the operating pressure angle b! It is expected that the bearing stress calculated in GEARS, which is based upon cam and follower principle, should be accurate within 10%. A spur gear calculator uses these parameters to generate the involute tooth form that's the right size and shape to take into your CAD software, or straight to a CNC router or laser cutter. Only in the case of non-corrected standard gears are both manufacturingclearance and operating clearance identical. Design & Manufacturability Involute Gear Cutters Find the right Spur Gear Calculator from our full list of free tools For a quick measurement of your gear across a fixed number of gear teeth, you can use our Gear Span Measurement Calculator and a set of calipers to find these measurements. + The result is dimensionless and equal to \thicksim 0.014 0.014. Let's draw the perpendicular to the line of centers passing through the pitch point. Free gear calculation software, calculate splines, calculate dimention over pins. Addendum modification and undercut If equation (\ref{p1}) is divided by equation (\ref{p0}), then the circumferential pitch p0 can be used to establish a connection between an arbitrary diameter d and the resulting circular pitch p: \begin{align}&\frac{p}{p_0} = \frac{d}{d_0} \\[5px]\label{pitch}&\boxed{p = \frac{d}{d_0} \cdot p_0} \\[5px]\end{align}. Whilst the output data in this calculator is completely accurate, i.e. We call the origin point SSS, then choose a point PPP on this curve. Just for fun. Order on Line 20 Pressure angle involute gear cutters Macmillan, 1975. If you are interested in other calculators, check our gear ratio calculator, the gear ratio speed calculator, or . It has already been explained in the article Profile shift that the backlash-free meshing of corrected gears results in a reduction of the tip tooth clearance in comparison to the backlash-free meshing of standard gears, since the change in centre distance is smaller than the sum of the profile shifts. Gear Calculator / Generator Notes for the wood shop or anyone using an endmill to make the cut:The bit size is a very important consideration! }{=} c \\[5px]&a m \cdot \left( \frac{z_1}{2} + x_1 1 \right) \frac{d_{a2^\text{*}}}{2} = 0 \\[5px]\label{da2}&\boxed{d_{a2}^\text{*} = 2 a m \cdot \left(z_1 + 2 x_1 2 \right) } \\[5px]\end{align}. If you'd like to support this site, please consider t: pinion [plate] thickness (tooth width) How to Model Globoid Worm Gears in Blender, How to Model a Bevel Gear Drive in Blender, How to Model a Planetary Gear Drive in Blender, How to Model a Hypocycloid Drive in Blender, How to Model a Hypoid Gear Drive in Blender, How to Model an Eccentrically Cycloidal Drive, How to Model a Rack-and-Pinion in Blender, How to Model Involute Gears Instantly in Blender, How to Model Internal/External Gears Instantly, How to Model Hyperboloidal Gears in Blender, How to Model Threaded Surfaces in Blender, How to Model Throated Worm Instantly (2.8+), How to Animate a Split-Flap Display in Blender, How to Model a Technical Drawing in Blender, How to Model Non-Circular Gears in Blender, How to Model a Tricky Part Based on a Drawing, How to Model Complex Parametric 3D Surfaces, Instant Straight and Helical Gear Calculator, Instant Internal/External Gear Calculator, 3D-Printable Eccentrically Cycloidal Model, 3D-Printable Tank with Single-Piece Tracks. The calculation of the root diameter d d,0 and the tip diameter d a,0 for standard gears has already been explained in the article Construction and design of involute gears. Spline stress calculation. Introduction. Changing the other two parameters ( and x) is not recommended. If the point P is located on the reference pitch circle of the gear, then the standard pressure angle0 is obtained! Profile Shift Default is 0 for most applications. Tooth Count is set with the parameter "n" for Gear 1 and Gear 2. Module is the ratio of the reference diameter divided by the number of teeth; so that a gear with a larger module will have a larger diameter. : a format for efficiently storing map tiles for use off-line on smart phones with FAT32 or similar file systems. Calculating the outer diameter, or OD, of your gear is important to ensure that you make the gear correctly and that it will mesh properly with its mate. The involute gear pressure angle is the fundamental parameter when designing the gear itself, since its value affects the tilting of the line of action and the behavior of the gear during its operations. The involute function is a function that takes as argument an angle the pressure angle and returns a value that corresponds to the width of the involute curve at that point. Calculation of the circular and the base pitch, Calculation of the profile shift coefficients, Excel spreadsheet for calculating involute gears. No problem with the method, which is fully understood, but I need a 20 degree PA, No8 gear cutter for 12-13t. The profile of helical gears are exactly the same as straight-cut gears but rotated through the helical angle. The involute angle thus corresponds to the operating pressure angle b. d: dedendum {bottom half of tooth - inside pitch diameter} Pressure Vessel The sum of the respective tooth thicknesses s1 and s2 thus corresponds to the circumferential pitch p on the operating pitch circles of the gears, which must be identical for both, otherwise the teeth could not mesh. The pitch point is the point on the line of centers where the circumferential speeds of the gears (you can learn how to calculate it with the circular motion calculator) match: this means that points on gears' edges travel at the same speed. Engineering Mathematics If you continue to use this website, we will assume your consent and we will only use personalized ads that may be of interest to you. Using our involute function calculator is really easy. Note that is in radians. Involute gear design and involute function. RPM: angular velocity. Gear Type External spur gears use a positive tooth count, while internal spur gears use a negative tooth count. Engineers use the shape of the involute of a circle to design the teeth of gears that touch only at one point during the entire contact time. The module of a gear controls its size. The default Manufacturing Profile Shift Coefficient is 0. : an introduction to the woodworking pages on my website. The determination of this contact ratio of two profile shifted gears will be shown in the following sections. As can be seen in Fig 3, mating gears of different diameters should have different profiles according to the appropriate involute curve for the diameter of the gear wheel concerned. Engineering Forum The operating pressure angle then also corresponds to the standard pressure angle 0. InvGearCtr 20 PA mm Module M0.7 #2 HSS TMX Involute Gear Cutters 20 Pressure Angle, Metric, Module M0.7 with 40 mm cutter diameter x 16 mm hole diameter, cutter # 2 for 14-16 range of teeth. Machine Design Apps Gear generation can also be produced with a gear shaper or planer machine. The distance T1E can be determined from the yellow triangle using the base circle diameter db1 and the (possibly shortened) tip diameter da1*: \begin{align}& \left( \frac{d_{a1}^\text{*}}{2} \right)^2 = \overline{T_1 E}^2 + \left( \frac{d_{b1}}{2} \right)^2 \\[5px]\label{11}&\underline{ \overline{T_1 E} = \sqrt{ \left( \frac{d_{a1}^\text{*}}{2} \right)^2 \left( \frac{d_{b1}}{2} \right)^2} }\\[5px]\end{align}. n: number of teeth Involute Spur Gear Profile Calculator - File Exchange - MathWorks The amounts da* to which the tip circles must be shortened are shown in the following sections. Spur Gear Calculator (tooth profile design and strength) Another way to think about it is positive profile shift numbers will allow for more backlash between two gears en-mesh. The operating tip tooth clearance cb, on the other hand, refers to the actual clearance in operation between the tip of the tooth of one gear and the root of the tooth of the mating gear. I've been around gear cutting tools and gear cutting my entire life -- but it's not the only thing I do. This is the core point of the peculiarity of involute gears: the contact between teeth happens only on a straight line obviously if the teeth' profiles match. However, it makes sense to assign the profile shift coefficientsevenly over the two gears, whereby the sum should not be much larger or smaller than one (i.e. Thermodynamics Involute Gear Cutters - Results Page 1 :: KBC Tools & Machinery If equation (\ref{f}) is applied in equation (\ref{cb}), then the operating tip tooth clearance cb can be determined from the manufacturing tip tooth clearance c as follows: \begin{align}&c_b = a \frac{\overbrace{ m \cdot (z_1+2x_1-2) -2c }^{d_{d1}}}{2} \frac{d_{a2}}{2} \\[5px]\label{cc}&\boxed{c_b = a m \cdot \left( \frac{z_1}{2} + x_1 1 \right) \frac{d_{a2}}{2} + c } \\[5px]\end{align}. Sincein this case the involute function inv() refers to the operating pitch circles d1 or d2, the involute angle corresponds to the operating pressure angle b. Input the gear's tooth count, pitch (or module), and pressure angle to calculate the pitch diameter, root diameter, and outer diameter. The tip of the string draws the involute. Your feedback and comments may be posted as customer voice. This is due to the fact that surfaces under high compressive load always deform significantly altering the contact area and therefore the resultant stress. Input the following parameters in our free gear dxf generator: - Laser cut gears out of wood or thin metal, - 2D or 3D modeling of gears for different simulations, - Understanding how gears work / why gears roll so well, - Start with a 2D sketch in SolidWorks, Fusion 360, Inventor, Revit, Onshape, SketchUp to buildup 3D gears. : improvements and tooling for my milling machine. Power Transmission Tech. Involute gear cutter calculations in Metric Engineering Book Store F: radial force separating pinion and gear (pushing their shafts apart) Auto position: Round to the nearest whole number. To use a gear in your chosen CAD system, you can download a DXF (or SVG). And noting that the pitch radius is r P = r B / cos , where is the pressure angle, then: r B cos = r B 1 + t P 2. The circumferential pitch(circular pitch) is the arc distance between two adjacent tooth flanks of the same direction. \begin{align}&\boxed{\epsilon = \frac{l}{p_b}} >1 \\[5px]\end{align}. Beam Deflections and Stress In some cases, however, the centerdistance to be achieved is fixed by the gearbox. The operating pitch circle diameters d1 or d2 in equation (\ref{pppp}) can be determined from the definition of the circular pitch p as the ratio of pitch circle circumference d and the number of teeth z (p = d/z). Re-Bar Shapes Apps We also see low resolution involute shapes that could function better if they had the correct geometry with sufficient data points defining the involute.Being members of the American Gear Manufacturers Association (AGMA) and having manufactured gears in most plastics and metals, the details count. The image below the table gives an indication of what the gear might look like. The previous figure illustrates the involute function in the context of the roll angle and pressure angle. 5. All angles for the involute function must always be given in radians! Helical gears are used to facilitate gear engagement and disengagement with minimal baulking, noise and or damage. Note that the involute function is not an algebraic function and therefore a reverse function cannot be derived. Machine Design: Theory and Practice. The reduction of the operating tip tooth clearance when corrected gears are engaging therefore makes it necessary to shorten the tip circles if the required tip tooth clearance c is to be maintained during operation. An increase in the pressure angle equals an increase in the width of the tooth. A gear wheel can be fully defined with as few as two parameters: the number of teeth (z) and module (m). Looking to 3D print, router, or laser cut a spur gear? Spur gears transmit power through parallel shafts. Finally some videos I found on youtube:Gear Generator How to Draw Perfect Gears (4:23)Laser Cut Gears (3:08)Prototype your gear sets in 2D (1:19). This explains why the involute function is so important. The following Excel spreadsheet for gear calculation offers the possibility to calculate different geometric parameters of involute gears: The calculations have not yet been completely checked for correctness! The application builds off the work of Dr. Rainer Hessmer and the. Electric Motor Alternators The circularpitch p on the operating pitch circles should not be confused with the circular pitch p0 on the reference pitch circles! Module (Pitch) this parameter sets the tooth size. Press the space key then arrow keys to make a selection. bigger (and more readable) version of it. r: profile radius of tooth (involute curve) I have a . Involute Function Calculator | Pressure Angle Physics The ratio of the line of contact l to the base pitch pb (distance between two adjacent contact points) is called contact ratio. Involute - Math of involute curves for mechanical gears - Drivetrain Hub Solving this equation for the operating pressure angle b in terms of the involute function inv(b) finally leads to: \begin{align}\notag\boxed{\text{inv}(\alpha_b) = 2 \frac{x_1+x_2}{z_1+z_2} \cdot \tan(\alpha_0) +\text{inv}(\alpha_0)} ~~~\text{and} ~~~\boxed{\text{inv}(\alpha_0) = \tan(\alpha_0)-\alpha_0} \\[5px]\end{align}. Input the gear's tooth count, pitch (or module), and pressure angle to calculate the pitch diameter, root diameter, and outer diameter. Most of the parameters are shown in the image on the left; you can click (or middle-click) on the image to see a The winners are: Opera for the best performance (shame on me, I never use it) and Firefox for the best looking SVG render. Make a Custom Gear. Engineering Standards Lubrication Data Apps The result is dimensionless and equal to 0.014\thicksim 0.0140.014. Involute gears are widespread and compose the vast majority of gears produced worldwide. Enter the desired parameters and click OK. In the article Profile shift of gears, the relationship between the profile shift coefficient x and the tooth thickness s0 has already been derived (with m as module of the gear): \begin{align}&\underline{s_0 = m \cdot \left(\frac{\pi}{2} +2 \cdot x \cdot \tan(\alpha_0) \right) } \\[5px]\end{align}. : metalworking-related stuff that doesn't fit elsewhere. You can then copy, paste and orientate each tooth according to its angular pitch, join them together and produce a complete or part gear. To make involute gear cutters, use this chart to make a hardened, relieved circular cutter ("cutter-cutter" dia.) Friction Engineering As long as your consent is not given, no ads will be displayed. Gear Ratio Calculator The starting point is the backlash-free meshing of the two gears, so that the tooth thickness on the operating pitch circle of one gear fits exactly into the tooth space on the operating pitch circle of the mating gear. Vibration Engineering Engineering Calculators In addition it let you compose full gear layouts with connetcted gears to design multiple gears system with control of the input/output ratio and rotation speed. The basis of this relationship is the identical basic circle diameter db which is identical both when considering the operating pitch circle (with the parameters d and and when considering the reference pitch circle (with the parameters d0 and 0): \begin{align}\label{base}&\overbrace{d \cdot \cos(\alpha)}^{\text{base circle diameter } d_b} = \overbrace{d_0 \cdot \cos(\alpha_0)}^{\text{base circle diameter }d_b} \\[5px]\label{z}&\underline{\alpha = \arccos \left(\frac{d_0}{d} \cdot \cos(\alpha_0)\right)} \\[5px]\end{align}. : a browser plug-in to allow you to blacklist bad ebay sellers. So we put the same attention to detail and mathematical skill to work for everyone. In equation (\ref{f}), z denotes the number of teeth, m the module, x the profile shift coefficient and c) the manufacturing tip tooth clearance. : an introduction to the metalworking pages on my website. Center Hole Diameter Central bore hole in each gear, for standard size wed recommend the Machinery's Handbook. I chose a Pitch diameter, P=76 mm, but obviously you can choose any value. Involute Gear Cutters . Feedback Advertising It is particularly useful for defining the parameters of a generating cutting tool capable of manufacturing cylindrical involute gears. The application itself, as well as the application specific source code is copyright (c) 2021 by Evolvent Design and is covered by the permissive MIT license. The taut string touches the circumference in the point TTT. Since the circular pitch p0 can also be expressed by the module m and the number (p0=m, see article Construction and design of involute gears), for the base pitch applies finally: \begin{align}\label{pb}&\boxed{p_b = \pi \cdot m \cdot \cos(\alpha_0)} \\[5px]\end{align}. This calculator generates the .DXF and .SVG files for making external spur gears, rack and pinion sets, and internal spur gears. Find, Compare, and Buy the GearCutting Tools You Need to Mill Gears, We built this spur gear calculator to ensure we had the right measurements for making gear blanks in our shop. t: circumferential thickness of tooth at pitch diameter If the centerdistance a is given in advance, then the operating pressure angle b can first be determined by solving equation (\ref{a}): \begin{align}\label{alpha}&\boxed{\alpha_b= \arccos \left(m \cdot( z_1 + z_2) \cdot \frac{\cos(\alpha_0)}{2 a} \right)} \\[5px]\end{align}. Calculate the key dimensions for your external spur gear. A point P on this involute can be described by the angle , which is spanned between the straight lines GP and GT. A gear's module is very nearly the inverse of the its diametral pitch, however module is expressed in millimeters while diametral pitch is 1/inches. Gears in SVG are measured in pixels, which is the value multiplied with the scale (Pixel per Unit) as it is displayed on the right side. In addition it let you compose full gear layouts with connetcted gears to design multiple gears system with control of the input/output ratio and rotation speed. : improvements and tooling for my bandsaw. The distance T2A can be determined by the blue triangle using the base circle diameter db2 and the (possibly shortened) tip diameter da2*: \begin{align}& \left( \frac{d_{a2}^\text{*}}{2} \right)^2 = \overline{T_2 A}^2 + \left( \frac{d_{b2}}{2} \right)^2 \\[5px]\label{2}&\underline{ \overline{T_2 A} = \sqrt{ \left( \frac{d_{a2}^\text{*}}{2} \right)^2 \left( \frac{d_{b2}}{2} \right)^2} }\\[5px]\end{align}. Free Gear Calculator 4. Involute gears can be easily generated by rack type cutters. Refer to the Catenary technical help page for a plotting procedure using Microsofts Excel spreadsheet. The red straight line represents the tensioned string as it wraps/unwraps. The operating pressure angle b has to be determined from an approximation method by the involute function: \begin{align}\label{inv}\text{inv}(\alpha_b) = 2 \frac{x_1+x_2}{z_1+z_2} \cdot \tan(\alpha_0) +\text{inv}(\alpha_0) \\[5px]\end{align}. The formulas given for the calculation of the contact ratio only apply to gears without undercut! Depending on your software, if the cutter is too large it will either over-cut the root and weaken the tooth, or leave a radius and not finish the involute profile or undercut. Now, P can be determined using the second of the polar formulae: = t arctan t. . The rack length defaults to the diameter of Gear 2. A gear wheel can be fully defined with as few as two parameters: the number of teeth ( z ) and module ( m ). In this construction, the angle of pressure is the angle TOP^=\hat{TOP} = \alphaTOP^=. the calculator, enter the module and number of teeth and the rest of the table should automatically update. Number of teeth* (N): Applications and Design Check out other tools I made:Print Charts, Flip.World, HTML Spirograph. + When using equation (\ref{ss}), it must be noted that the tooth thickness s0 on the reference pitch circle depends on a possible profile shift. One of the more common mistakes we see in simplified gear software is the lack of undercut in small tooth count gears. Involute Gear Cutters / DP and Module - RDG Tools Gears can be animated with various speed to demonstrate working mechanism. Electronics Instrumentation Learn about pinion generation gear cutting methods to manufacture spur gears, helical gears, and internal gears. Deutschman, Michels, Wilson. At this point, the angle between this line and the action line is called pressure angle. Gears can be animated with various speed to demonstrate working mechanism. Gear Generator The figure shows that the sum of the distances T1E (yellow triangle) and T2A (blue triangle) is greater by the amount of the line of contact l than the distance T1T2. Hardware, Metric, ISO The ratio of tooth count between two gears changes the relative speed of those gears by that ratio. . The manufacturing tip tooth clearance results from the tool profile during gear cutting. The involute function explained in the previous section can be used to determine the tooth thickness s on an arbitrary diameter d of a gear. Rounding tool allows you to round up or down any values. Input the center distance between the pinion and the gear. Input the number of teeth of the pinion and the gear. If a certain center distance is to be achieved by a profile shift, then the sum of the profile shift coefficients must satisfy the equation (\ref{x}). Having the right gear blank is an essential part of the gear-mkaing process, and helps ensure your gear is within tolerance. In the case of the point P0, which is located on the reference pitch circle, the involute angle 0 is then identical to the standard pressure angle 0, which is usually set to 0=0.349 rad (=20). The angles and 0 correspond to the angles that can be determined using the involute function inv() according to equation (\ref{involute}). 6. The gear calculator provides x,y drawing co-ordinates for both the pinion and the gear teeth. We have generated the assembly shown in Fig 5 using Excel and Xara computer programs. As shown in the article Construction and design of involute gears, the term p0cos(0) occurring in equation (\ref{pp}) corresponds to the base pitchpb and therefore corresponds the distance between two tooth flanks in contact on the line of action when meshing (see figure below). Copyright 2011-2023 A. S. Budden | All Rights Reserved, Design by 1234.info | Modified by A. S. Budden | XHTML 1.0 | CSS 2.0. : home page and list of updates to this site. Gear Design Equations and Formula | Circular Pitches and Equivalent Economics Engineering Just what you need to get your spur gear project started today. : maximum bending stress in tooth When cutting a spur pinion like the gear shown in Figure 1, undercutting occurs if you cut deeper . Center Distance Calculator | Evolvent Design y: vertical distance from centreline of tooth to centre of 'r' Heat Transfer making a small donation Therefore, for the operating pitch circle diameters of the two gears d1 and d2 applies: \begin{align}\label{dd}&d_1 = \frac{z_1 \cdot p}{\pi} ~~~~~\text{and}~~~~~d_2 = \frac{z_2 \cdot p}{\pi} \\[5px]\end{align}. F: factor applied to tooth dedendum ('d'), which should be 1 for a standard (full-height tooth), Common to Pinion and Gear: All calculated values in Table 4.1 are based upon given module m and number of teeth (z 1 and z 2).If instead, the modulem, center distance a and speed ratio i are given, then the number of teeth, z 1 and z 2, would be calculated using theformulas as shown in Table 4.2.. Table 4.2 The Calculations for Number of Teeth \begin{align}\label{involute}&\boxed{\text{inv}(\alpha) = \tan(\alpha)-\alpha} = \varphi~~~\text{involute function} \\[5px]\end{align}. Involute Gear Calculator The angle describes the thickness of the involute tooth, so to speak. ZAKGEAR Calculators Using: = r B 1 + t 2. : pitch diameter of tooth Steel is a popular choice when creating metal gears due to its high strength and low cost. Welding Stress Calculations Diametral Pitch Teeth/in. For the line of contact l therefore applies: \begin{align}&\overline{T_1 E} +\overline{T_2 A} l =\overline{T_1 T_2} \\[5px]\label{0}& \underline{ l = \overline{T_1 E} +\overline{T_2 A} \overline{T_1 T_2} } \\[5px]\end{align}. As explained in the article Profile shift, the tip tooth thickness should be at least 0.2 times the module. The involute function can also be used to express the relationship between pressure angle and roll angle. This also generates the tooth dimensions: addendum, dedendum, working depth, and whole depth. The spline connection in Figure 1 is neither centering on the flanks nor on its major or minor diameters. Involute Gear Design Equations and Calculator