Patent Publication Number: US-11650048-B2

Title: Apparatus and method for coaxtailly aligning two rotatable shafts

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation-in-part of U.S. application Ser. No. 16/915,728 filed Jun. 29, 2020, which claims the benefit of U.S. provisional application Ser. No. 62/869,768 filed Jul. 2, 2019, the disclosures of which is hereby incorporated in its entirety by reference herein. 
    
    
     TECHNICAL FIELD 
     This application relates to an apparatus and a method for coaxially aligning two rotatable shafts, particularly shafts of a rotary machine, such as a pump and a motor, connected by a rotary coupling. 
     BACKGROUND 
     When two rotatable shafts are coaxially coupled together it is very important to minimize coaxial misalignment. Even a small amount of misalignment can result in power losses, unnecessary bearing loads and premature coupling failure. Accordingly, the shafts must be carefully initially aligned and periodically inspected and adjusted as necessary. 
     Motor driven pumps used in municipal water systems and in sewage collection and treatment facilities are typical users of large motor and pump pairs which must be maintained in proper coaxial alignment. Further, many industrial and chemical facilities use very large motor and pump pairs, turbines and generators, motors and compressors, and other co-axially aligned rotatable machines which need to be maintained in proper coaxial alignment. 
     Various devices have been used to align two coaxial rotatable shafts in the past ranging from traditional mechanical surface plate gauges to a laser and a detector mounted to adjacent shafts to be inspected while the shafts are manually rotated as illustrated in U.S. Pat. No. 8,533,965. 
     SUMMARY 
     An apparatus and method for aligning two coaxially coupled rotatable shafts is provided. Alignment can be, and is preferably, measured while the shafts are rotating in their normal operating condition. A base is positioned adjacent to the shafts to be aligned. The base supports a servo operated positioning device which is movable along a longitudinal axis parallel to the axis of the shafts, and movable to vertically position spots on the shaft measured by a laser range finder (LRF) adjacent to the two rotatable shafts. The LRF measures the distance between the LRF and a spot on the shaft. A controller having a processor and memory communicates with the positioning device to cause the LRF to scan a plurality of spots on the shafts spaced over a vertical range and collects data at two or more axial positions on each shaft. At each position the LRF measures the distance to the shaft and stores the measurement and location data. The spot measured by the LRF is vertically repositioned and the measurement and storing steps are repeated over a scan distance sufficient to provide enough data to determine the location of the shaft center. The processor then calculates and compares the shaft centerlines and determines the necessary adjustments needed to move the shafts into alignment. 
     An exemplary embodiment of the apparatus for aligning two rotatable shafts has a base which is positionable adjacent to two rotatable shafts while they are coaxially coupled together and rotating. A servo operated positioning device is attached to the base, movable along a longitudinal X-axis parallel to the axis of the rotating shafts, and movable vertically along a Y-axis. A laser range finder (LRF) is affixed to the positioning device and spaced a distance from the two rotating shafts, to measure the distance between the LRF and a spot on the rotating shafts parallel to a Z-axis. A controller is provided which communicates with the positioning device and the LRF. The controller has a processor programmed to position the LRF at a first axial location on a first one of the rotating shafts, measuring distance to the shaft and stores the measurement and spot location data. The controller vertically repositions the LRF and repeats the measurement and data storage steps. Vertical repositioning and measurement steps are repeated until enough data is collected to determine the location of the shaft center at the first axial location. The processor is programmed to reposition the LRF at a second X-axis location on a first one of the rotating shafts and the Y-axis scan is repeated and the location of the first shaft axis is calculated. The processor is programmed to reposition the LRF at a third and fourth X-axis location on a second one of the rotating shafts and the Y-axis scan is repeated and the location of the second shaft axis is calculated. The alignment of the two shafts axes are compared. The processor then determines the adjustment of one of the two shafts that is necessary to move the shafts in to coaxial alignment. 
     Another exemplary embodiment of the apparatus for aligning two rotatable shafts has a base which is positionable adjacent to two rotatable shafts while they are coaxially coupled together and rotating. A servo operated positioning device, in the form of a multi axis robotic arm, is attached to the base, movable along a longitudinal X-axis parallel to the axis of the rotating shafts. The robotic arm has an end which is movable along at least the Z and Y axes using servo motors or other means of electronic positioning. Preferably, the robotic arm also operates along the X axis as well. A laser range finder (LRF) is pivotably affixed to the end of the robotic arm to measure the distance between the LRF and a spot on the rotating shaft. A controller is provided which communicates with the robotic arm and the LRF. The controller has a processor programmed to position the LRF at a first axial location on the first one of the rotating shafts. The robotic arm positions the LRF adjacent to the rotating shaft to measuring distance between the shaft and the LRF. The LRF measurement and the LRF location on the robotic arm end is used to determine and store location data of a spot on the shaft peripheral surface. The controller repositions the robotic arm and the LRF to measure a different spot on the peripheral surface and repeats the measurement and data storage steps. The repositioning and measurement steps are repeated until enough data is collected to determine the location of the shaft center at the first axial location. 
     The processor is programmed to reposition the LRF at a second X-axis location on a first one of the rotating shafts and the scan is repeated and the location of the first shaft axis is calculated. The processor is programmed to reposition the LRF at a third and fourth X-axis location on a second one of the rotating shafts and the scan is repeated and the location of the second shaft axis is calculated. The alignment of the two shafts axes are compared. The processor then determines the adjustment of one of the two shafts that is necessary to move the shafts in to coaxial alignment. 
     A method for aligning two rotating shafts which are coaxially coupled together is disclosed which includes providing a positioning device attached to a base to be placed adjacent to the shafts to be aligned. The positioning device has a holder movable along a longitudinal axis parallel to an axis of two axially coupled rotating shafts, and movable vertically to position a laser range finder (LRF) affixed to the positioning device and spaced a distance from the two rotating shafts. The LRF measures the distance between the LRF and a plurality of vertically spaced spots on the rotating shafts. A controller, having a processor and memory, is provided which communicates with the LRF and a user interface. The LRF is positioned at a first axial location on a first one of the rotating shafts, the controller communicating with the LRF to measure distance to a spot on the shaft and stores the measurement and spot location data. Data is collected at a minimum of three spot locations or until enough data is collected to determine the location of the shaft center at the first axial location. This process is repeated at a second X-axis location on the first shaft and at a third and fourth X-axis location of the second shaft. The processor then calculates the centerline of the two shafts using stored measurement and spot location data using a best-fit circle algorithm to define the axis of the two shafts and then determines the adjustment of one of the two shafts needed to move the shafts in to proper alignment. 
     In the robotic arm embodiment, the LRF is moved in both the Z and Y directions. Preferably the LRF axis is oriented perpendicular to the shaft axis prior to making measurements. 
     In an alternative embodiment the diameter of the shaft is known or is measured and input into the processor. With the shaft diameter known it is only necessary to collect data at a minimum of two Y-axis locations. 
     In yet another embodiment rather than vertically moving the LRF, the LRF is located at the approximate shaft center height. The beam of LRF then pivots about an axis generally parallel to the shaft to scan a plurality of measurements at one or more Y-axis locations. The pivoting LRF can also be used in a system of unknown shaft diameters if data is collected at three Y-axis locations. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a top view of an alignment apparatus adjacent a motor driven pump; 
         FIG.  2    is a side view of the alignment apparatus of  FIG.  1   ; 
         FIG.  3    is a sectional view taken along line  3 - 3  of  FIG.  2   ; 
         FIG.  4    is an enlarged section of  FIG.  3    showing the laser range finder (LRF) scanning motion; 
         FIG.  5    is a histogram of the data collected at one scan point; 
         FIG.  6    is X-Y plot of the average scan data at one shaft position to which a circle is fit in order to locate the shaft center; 
         FIG.  7    is a block diagram of the use of the alignment apparatus to perform the shaft alignment method; 
         FIG.  8    is a schematic of the components making up the alignment apparatus. 
         FIG.  9    is an alternative embodiment of the alignment apparatus having laser range finder (LRF) with a pivoting scanning motion; 
         FIG.  10    illustrates the location of the centerline of a shaft of known diameter using two points on the shaft surface; 
         FIGS.  11 A and  11 B  are a top views of an alternative alignment apparatus embodiment adjacent a motor driven pump: 
         FIG.  12    is a perspective view of a multi axis robotic arm; 
         FIG.  13    is a side view of the multi axis robotic arm; 
         FIGS.  14 A and  14 B  are views showing the effect of LRF misalignment with the shaft; 
         FIG.  15    is another alternative alignment apparatus embodiment adjacent a motor shaft; 
         FIG.  16    is a top plan view of the alignment apparatus embodiment of  FIG.  15   ; 
         FIG.  17    is a X-Y plot of the average scan data at three positions on the shaft. 
     
    
    
     DETAILED DESCRIPTION 
     As required, detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention that may be embodied in various and alternative forms. The figures are not necessarily to scale; some features may be exaggerated or minimized to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the present invention. 
     The disclosed preferred embodiment of the apparatus  10  and the method are used to calculate the adjustments necessary to realign two coupled, rotatable shafts which are inspected while “hot and rotating” in a steady state operating condition. The two shafts are typically associated with a large co-axially aligned rotating machines such as motor and pump pairs, turbines and generators, and motors and compressors, and other co-axially aligned rotating machines. which need to be maintained in proper alignment. While a motor M and pump P are described in this preferred embodiment the claims are not limited to any specific types or size of co-axially aligned rotating machines. Similarly, the disclosed example is oriented horizontally however the apparatus and method could also be used in machines of other orientations such as a vertical turbine and generator. The apparatus and method can be used on the two shafts when not rotating but it has been found that more practical results can be achieved while the shafts are rotating. 
     In the sample embodiment shown in  FIG.  1    motor M drives the pump P. The pump shaft  12  is typically part of a pump assembly P, that is coupled to inlet and outlet pipes and for all intents and purposes is immovable and will remain “stationary”. The motor shaft  14  is part of a motor assembly M and is coupled to the pump shaft  12  by a pair of couplings  16 ,  18  and one or more flexplates  20 . Slight adjustments to the position of the motor M can be made by loosening the bolts  22  holding the motor feet  24  to the foundation  26  and shifting the motor by shimming the motor feet. Great care is taken to align the two shafts in all dimensions before turning on the motor. Shims  28  are placed under four feet  24  of the motor M to adjust the height (Y-axis), and adjustment screws  30  (shown in  FIG.  3   ) are used to move the motor in-and-out laterally (Z-axis). 
     The apparatus  10  computes the amount of adjustment necessary to reposition the motor feet along the Y-axis and Z-axis to realign the two shafts by measuring shaft location while the motor and pump is “hot and rotating”. 
       FIG.  1    illustrates a top plan view of a large electric motor M connected to a pump P. A side view is shown in  FIG.  2    illustrating the positioning apparatus  10  relative to the motor and pump and the various measurement locations. Apparatus  10  conducts a measurement scan of at least four axially spaced locations, two on the pump shaft and two on the motor shaft. The measurements are made using a non-contact laser range finder (LRF)  30 . The LRF is attached to a positionable base  32  adjacent to the motor M and pump P as shown. The LRF is movable relative to the motor axis by a multi axis positioning device. An X-servo  34  connected to a base  32  moves the LRF parallel to the motor axis. The LRF is movable vertically in the Y direction along a vertical column  36  by a Y-servo  38  connected to the X-servo  36 . 
     As illustrated in  FIG.  3    the LRF measures the distance between the LRF and the pump shaft  12  at point PS. Optionally the LRF is provided with level sensor with a micro level adjustment servo  40  to maintain the LRF and the produced laser output beam exactly horizontal. Another optional feature is a Z-axis servo  42  enabling the LRF to be positioned close to the rotating surface, maintaining the scan distance to less than 2 inches, preferably less than 1 inch. By minimizing the Z distance measurement accuracy can be significantly improved by selecting a LRF having a short range. 
     The following input parameters are input into the controller  44  via a user interface before running the alignment scan. Note that X-axis refers to left-and-right in above  FIGS.  2  &amp;  3   , Y-axis to up-and-down in  FIG.  2   , and Z-axis to in-and-out best seen in  FIG.  1   . 
     PSx: X-position on pump shaft (or similar), closest to pump 
     PCx: X-position on pump side of coupling (or similar) 
     MCx: X-position on motor side of coupling 
     MSx: X-Position on motor shaft (or similar), closest to motor 
     MF: distance from inside edge of pump coupling to front feet on motor 
     MR: distance from inside edge of pump coupling to rear feet on motor 
     LE: distance from laser reading point PCx to inside edge of pump coupling 
     As previously stated, the pump P should be considered stationary. Therefore, the imaginary centerline of the pump shaft is the foundation used for all calculations. The motor M must be moved through shims  28  and adjustment screws  30  to align or realign with the pump. 
     First, the X-values for PS, PC, MC, and MS are entered into the system, typically by moving the LRF (through the User Interface UI) to the preferred positions and storing these X-values. Once the scan is initiated, the laser scans the surface (up and/or down) at PSx and PCx as shown in  FIG.  4   , collecting thousands of data points on the surface of the shaft or coupling. At each data point hundreds of readings are made, preferably at least 200, and an average or mean of the readings are stored. Optionally, the lowest and highest readings are discarded to improve accuracy however a number of other techniques can be used to improve accuracy of the stored data point. The Y-servo  38  moves the LRF to the next reading site and another average or mean data point is stored. Preferably the X movement increment is over 3 inches, and more preferably over 4 inches. 
     The Y-servo in the illustrated embodiment has a travel of 1.0 inches which is sufficient for many commonly used shaft sizes. Ideally the Y-servo scan distance is at least 20%, preferably over 20% and less than 50% of the radius of the rotating section being scanned. When used on large diameter shafts and couplings the scan distance increases accordingly. The scan is done while the motor is on and the shafts are rotating and have reached a steady state operating condition. The collected averaged scanned measurements at each point PS, PC, MC, and MS are evaluated programmatically in a Z-Y diagram as shown in  FIG.  6   . This series of data points form a curved circular segment  42  to which a circle is fit to using a best-fit algorithm. Preferably, 50 to 250 data points make up the circular segment. However, it is possible to fit a circle to as few as three data points as illustrated in bold in  FIG.  6   . 
     Using a best-fit-circle algorithm, such as Levenberg-Marquardt, the center point  40  of the shaft can be calculated in three dimensions, at both PSx and PCx. The best-fit circle  44  has a center point  40  which defines a point on a line representing the axis of the shaft, as illustrated in  FIG.  6   . These points provide two absolute points in three-space (PSx, PSy, PSz) and (PCx, PCy, PCz). Two 3D points defines a 3D line, and this line determines the pump shaft centerline. More than two points could be used as well, meaning additional intermediate points between PS and PC. In this case, a best-fit-line algorithm, such as least squares, may be used to determine a more precise centerline, however two points is satisfactory. 
     Important outputs from the algorithms include the pump pitch (Y-axis slope) and the pump yaw (Z-axis slope) relative to apparatus  10 , computed from (PCy−PSy)/(PCx−PSx). Pump yaw is computed from (PCz−PSz)/(PCx−PSx). Note there is no need for the pump or apparatus to be perfectly level since all measurements are relative. We now have two 3D points, that define an imaginary centerline in three dimensions that extends from the pump through the motor. Next, we can align the shaft  14  of the motor M to match the pump shaft  12  in all three dimensions. 
     Scanning the motor shaft  14  is done similar to the scanning of the pump shaft  12 . The LRF scans the motor shaft  14  or the motor coupling  18 , or at two or more spaced apart X-axis points (i.e. MCx, MSx, etc.) and computes at least two center points MCx, MCy, MCz and MSx, MSy, MSz and the resultant motor centerline which is best fit using a best-fit-line algorithm. Like with the pump, the motor&#39;s relative pitch (MSy−MCy)/(MSx−MCx) and yaw (MSz−MCz)/(MSx−MCx) are computed for the motor&#39;s centerline. Even after precise “cold” alignment, the motor centerline is typically out of alignment with the pump centerline once “hot and running”. To be in near-perfect alignment, the motor must be shut down and the feet adjusted (up/down and in/out) so that its centerline is aligned with the centerline of the “stationary” pump. 
     We have computed the two 3D points that define the pump shaft centerline. We have also computed the pump pitch and yaw relative to the apparatus. To align the two shafts, we need to make the motor pitch and yaw the same as the pump pitch and yaw, and that the two shaft axes intersect at the coupling connecting the shafts together. A translation (up/down, in/out) may also be required of the motor shaft in addition to adjusting the pitch and yaw to obtain proper co-axial alignment. For both MC and MS, we can compute the ideal 3D coordinates that would put the motor shaft in perfect alignment with the pump shaft. We will call these ideal coordinates MCx, MCyi, MCzi and MSx, MSyi, MSzi. 
     It should be noted that the 3D alignment problem can be broken down into two, 2D alignments, namely up/down and in/out (the motor is not adjusted left/right once coupled to the pump). First, we will discuss the adjustment calculations in the Y-axis (i.e. pitch alignment) and separately the adjustment calculation for the Z-axis (i.e. yaw alignment). We are solving for how much to adjust the feet of the motor such that the two center points at MCx, MCyi, MCzi and MSx, MSyi, MSzi fall perfectly on the imaginary extended centerline projected out from the pump. 
     Pitch Calculation: A 2D line can be described by the equation y=mx+b, where m is the pitch and b is the y-intercept. For pump pitch, we have two baseline points PSx, PSy and PCx, PCy which can be used to compute the perfect pitch m=(y2−y1)/(x2−x1) and the y-intercept (b=y−mx). With m and b known, we can compute the ideal (i.e. aligned) y-value (yi) for any x-value, specifically at MCx and MSx. This provides us with MCx, MCyi and MSx, MSyi. 
     Yaw Calculation: Similarly, we can represent the pump&#39;s 2D yaw line with the equation z=nx+c, where n is the yaw and c is the z-intercept. For pump yaw, we have two baseline points PSx, PSz and PCx, PSz which can be used to compute the perfect yaw n=(z2−z1)/(x2−x1) and the z-intercept (c=z−nx). With n and c known, we can compute the ideal (i.e. aligned) z-value (zi) for any x-value, specifically at MCx and MSx. This provides us with MCx, MCzi and MSx, MSzi. 
     By combining the results from the ideal pitch and yaw calculations, we now have 3D coordinates MCx, MCyi, MCzi and MSx, MSyi, MSzi, and any additional points in between. These are where the motor center points need to be in order for the two shafts to be in perfect alignment, and typically vary from MCx, MCy, MCz and MSx, MSy, MSz which is where they were measured to be. 
     Calculating the difference between the existing, measured motor center points MCx, MCy, MCz and MSx, MSy, MSz and their ideal, aligned locations MCx, MCyi, MCzi and MSx, MSyi, MSzi is simple subtraction. The only complication is that the motor feet adjustments are not directly below MC and MS. Instead, the adjustments are some distance away which creates a “lever arm” at MF and MR. 
     However, we can use a simple ratio to determine the amount of adjustment at some point further away. We know the distance from PS-to-MC is (PSx−MCx). We also know the distance from PS-to-MF is ((PCx−PSx)+LE+MF). If the second distance is twice the first, for example, then we must double the amount of adjustment at the front foot. Similarly, we know the distance from PS-to-MR is ((PCx−PSx)+LE+MR). If the distance to MR is three times the distance to MC, for example, then we must triple the amount of adjustment at the rear foot. This is true for both pitch adjustments (i.e. shims) and yaw adjustments (screws  30 ). 
     The apparatus uses precise positioning of the laser along the X-axis, surface scanning in the Y-axis using a LRF making high-precision laser distance measurements in the Z-axis and precise incremental repositioning of the laser along the Y-axis to establish a baseline position for the pump and motor shaft surfaces. Outliers are filtered from the raw data and the best available measurement data is run through a best-fit-circle algorithm to determine two or more center points for each shaft. Adjustments to the motor feet are then calculated, and the motor can be put into near perfect alignment with the pump. No other alignment system can measure alignment of a motor and pump shaft while “hot and running” or align two shafts to this level of precision. 
     The basic components of the measurement apparatus  10  are illustrated schematically in  FIG.  8   . The apparatus  10  has a controller  50  having a processor  52  and a memory  54  for controlling the movement of the LRF, possessing the collected data, calculating the position of the pump and motor shafts and calculating the necessary movement to co-axially align the shafts. The controller is coupled to the X-servo  34 , the Y-servo  38  and to a user interface UI. The UI, which can be a keyboard and monitor of a touch screen, enables the user to cause the controller to position the LRF at the four data collection positions PS, PC, MC, and MS before the start of the measurement procedure. Alternatively, the UI can be a laptop computer, a smart phone or tablet. Preferably the X-servo moves the LRF between the four PS, PC, MC, and MS. However, in a low-cost embodiment the LRF could be manually moved along the base on a precision track and positioned at stops precisely located at the four spaced apart measurement locations. In even a lower cost point apparatus the Y-servo could be replaced with a mechanical screw and guide way similar to that use in a lathe or other machine tools to manually position the LRF at three or more precisely spaced apart locations enabling a best-fit curve to be fit to the three points in order to define the shaft center. 
     The method for aligning two rotating shafts which are coaxial coupled together is shown in block diagram in  FIG.  7   . The method comprises the steps of: 
     providing a positioning device attached to a base, having a holder movable along an X-axis parallel to an axis of two axially coupled rotating shafts, and movable along a Y-axis to position a laser range finder (LRF) affixed to the holder a paced a distance from the two rotating shafts to measures the distance between the LRF and a plurality of vertically spaced spots on the shafts| 
     providing a controller, having a processor and memory, communicating with the LRF and a user interface| 
     positioning the LRF at a first X-axis and Y-axis location on a first one of the rotating shafts, causing the controller communicating with the LRF to measure the Z-axis distance to a spot on the shaft and storing the measurement and spot location data; 
     repositioning the LRF along a Y-axis, and repeating the measurement, storing, steps at least until enough data is collected to determine the location of the shaft centerline at the first axial location; 
     positioning the LRF at a second X-axis location on the first rotating shaft, causing the controller to measure distance between the shaft and the LRF and storing the measurement and spot location data 
     repositioning the LRF along the Y-axis and repeating the measurement, storing steps and repeating until enough data is collected to determine the location of the shaft centerline at the second X-axis location 
     positioning the LRF at a third X-axis location on a second one of the rotating shafts, causing the controller to measure distance between the shaft and the LRF and storing the measurement and spot location data 
     repositioning the LRF along the Y-axis and repeating the measurement, storing steps and repeating until enough data is collected to determine the location of the shaft centerline at the third axial location 
     positioning the LRF at a fourth axial location on the second rotating shaft, measuring causing the controller to measure distance between the shaft and the LRF and storing the measurement and spot location data 
     repositioning the LRF along the Y-axis and repeating the measurement, storing steps and repeating until enough data is collected to determine the location of the shaft centerline at the fourth axial location; and 
     calculating in the processor the centerline of the two shafts at each of the four X-axis locations using stored measurement and spot location data using a best-fit circle algorithm to define two spaced apart axis location points for each shaft and determining the adjustment of one of the two shafts needed to move the shafts in to coaxial alignment and outputting the adjustment information to the user via the user interface. 
     In another embodiment, shown in  FIG.  9   , rather than vertically moving the LRF, the LRF is positioned in a fixed located at the approximate shaft center height. The beam of LRF is then pivoted over an angle θ about an axis generally parallel to the shaft to scan a plurality of Y-axis locations. Pivoting the LRF causes the laser beam emitted from the LRF to measure a spot on the rotatable shafts to move in the Y direction relative to the rotatable shafts. The shaft centerline is then determined as described above or as described in the following paragraph. 
     In another an alternative embodiment the diameter of the shaft is known in advance or is measured and input into the processor. When the shaft diameter is known it is only necessary to collect data for at least two Y-axis locations. The center location of a known diameter shaft can be determined with only two points as shown in  FIG.  10   . If the two measurement points are the same distance from the LRF dimension the distance between the points is the chord length C of a line extending through the shaft. A line through the LRF and the center of chord C goes through the center of the shaft as illustrated in  FIG.  10   . With the radius R known the shaft center can be located relative to the LRF position using simple algebra, the Pythagorean theorem, geometry, and the chord length equation. Alternatively, the two points can be used to locate the shaft center by fitting a known diameter arc to the two points. When the shaft diameter is known, much less data needs to be collected and the circle fitting calculations are greatly simplified. 
     In another embodiment of the apparatus  60 , shown  FIG.  11 - 14   , the servo operated positioning device, is provided by a multi axis robotic arm  62  which provides another type of multi axis positioning device. The robotic arm  62  is affixed to a base  64  stationarily located relative to the axes of the rotating shafts to be aligned. The robotic arm  62  is made up of a lower member  66  attachable to the base  64  in one or more fixed locations. Preferably, atop the lower member  66  is a swivel plate  68  rotatable about a vertical 1 st  axis by a 1 st  servo motor. Pivotably attached to swivel plate  68  is a proximal end of lower arm  60 . The proximal end of lower arm  70  is rotatable about a 2 nd  axis, preferably parallel, to the swivel plate  68  by a 2 nd  servo motor. The distal end of the 1 st  arm is pivotable attached to the proximate end of an upper arm  72  and rotated about a horizontal 3 rd  axis by a 3 rd  servo motor. The distal end of the upper arm  72  is pivotably connected to a LRF and rotatable about a horizontal 4 th  axis by a servo motor. Preferably the LRF is rotatable about a 5 th  axis perpendicular to the 4 th  axis by a 5 th  servo motor. The 5 th  axis enables the beam of the LRF to maintain a perpendicular position to the shaft after moving in an X-direction between two t spaced axial shaft locations without moving the robot lower member  66  along base  64 . 
     The servo motors in the robotic arm enable the LRF to be precisely located in space and be circumferentially moved about the shaft. The laser beam formed by the LRF can be oriented perpendicular to the shaft. The use of a robotic arm enables the LRF to be located relatively close to the shaft, preferably within 40 mm, and more preferably with 20 mm, resulting in a high degree of accuracy. Of course, the multi axis robotic arm embodiment of the apparatus  60  can be used in the manner of the apparatus embodiments disclosed in  FIGS.  1 - 10   , where the distance from the LRF and the spot on the shift being measure is not held constant. 
       FIG.  11    is a plan view of robot arm  62  attached to base  64  which laterally positioned relative to motor M and pump P having a pair of generally coaxial shafts  12 ′ and  14 ′ interconnected by a coupling C. The robotic arm  62  is positioned on the base  64  outboard of the shaft  12 ′ of pump P. Preferably robot arm  62  can reach both the first and second X-axis location where measurements are taken. Alternatively, the robot arm  62  can be repositioned on the base  44  outboard using an X-axis servo. When propagating the movement of the LRF between X-axis locations care should be taken to avoid striking the LRF or the robot arm on the shafts, the coupling or any safety guards. Optionally a vision system having a camera or LIDAR sensor coupled to the controller to monitor the position of the LRF and the robot arm relative to the surroundings to avoid a strike. 
     The robot arm  62  mounted on carriage  63  can be moved along the base  64 , as shown in  FIGS.  11 A and  11 B , to a position outboard of the motor M shaft shown in phantom outline. From this position robot arm  62  can reach both the third and fourth X-axis locations. Alternatively, the robotic arm  62  mounted on carriage  63  can be repositioned on the base  64  outboard using an X-axis servo. By moving the robotic arm  62  between measurements at the first and second and third and fourth X-axis locations the arm can remain generally perpendicular to the shaft minimizing the need to adjust the position of the LRF about the 5 th  axis to be perpendicular to the shaft. 
       FIG.  12    is an example of a servo operated multi axis robotic arm  62  which is attachable to a base  64  for supporting a laser range finder (LRF) on the arm distal end (free end). The robotic arm distal end is pivotably attached to a laser range finder (LRF) to orient the LRF perpendicular to and space a distance from the rotating shaft to being measured. The LRF measures the location of a plurality of peripherally spaced spots on the shafts at two axial positions on each shaft. 
       FIG.  13    is a side cross-sectional elevation of multi axis robotic arm  62  with the LRF positioned in close proximity to the shaft to be measured. In order to achieve high accuracy, The LRF is preferably within 40 mm, and more preferably with 20 mm of the shaft. The LRF is moved about the periphery to a plurality of positions as illustrated. To locate the shaft center at least three spots on the shaft periphery must be measured. If the shaft diameter is known only two spot need to be measured. For accuracy purposes many more spots are measure to better fit a curve to the data. Preferably, at least 10 spots are measured over 45 degrees of the shaft circumference. More preferably, over 200 spots are measured over 90 degrees of the shaft circumference for best accuracy. 
       FIG.  14 A  illustrates a slight LRF misalignment from the ideal perpendicular alignment to the shaft. This will result in the section of oval shape, shown in exaggerated form. Once the LRF is aligned in a perpendicular manner as shown in  FIG.  14 B  the cross section is circular. The 5 th  axis servo motor at the arm distal end enables the beam of the LRF to be maintained perpendicular to the shaft after moving between two adjacent axial shaft locations without moving the robot arm  62  about a vertical axis relative to the base  64 . 
     The method for aligning two rotating shafts which are coaxial coupled together using the multi axis robotic arm embodiment of the apparatus  60  has an initial step of providing a servo operated multi axis robotic arm attachable to a base affixed in spaced relation to axis of two axially coupled rotating shafts oriented along a Y-axis. The robotic arm has a distal end pivotably attached to a laser range finder (LRF) to orient the LRF a distance from the two rotating shafts to measures the location of a plurality of peripherally spaced spots on the shafts on two axial positions on each. 
     A controller is provided, having a processor and memory, communicating with the servo motors of the multi axis robotic arm, the LRF and a user interface. The controller positions the LRF at a first X-axis location on a first one of the rotating shafts. The controller communicating the servo motors of the multi axis robotic arm, and the X-axis servo to move the LRF peripherally about the shaft and while storing the LRF location and the measured distance to a plurality of peripherally spaced spots. 
     Next the controller positions the LRF at a second X-axis location on the first rotating shaft, causing the controller communicating the servo motors of the multi axis robotic arm, to move the LRF peripherally about the shaft and storing the LRF location and the measured distance to a plurality of peripherally spaced spots. 
     The controller moves the LRF to a third X-axis location on a second one of the rotating shafts, causing the controller communicating the servo motors of the multi axis robotic arm, to move the LRF peripherally about the shaft and storing the LRF location and the measured distance to a plurality of peripherally spaced spots. 
     The controller moves the LRF to a fourth X-axis location on the second rotating shaft, measuring causing the controller communicating the servo motors of the multi axis robotic arm, to move the LRF peripherally about the shaft and storing the LRF location and the measured distance to a plurality of peripherally spaced spots. 
     With the data collected the controller calculates, in the processor, the centerline of the two shafts at each of the four X-axis locations using stored LRF location and the measured distance to a plurality of peripherally spaced spots, using a best-fit circle algorithm to define two spaced apart axis location points for each shaft. The processor determines the adjustment of one of the two shafts needed to move the shafts in to coaxial alignment. The adjustment information needed to align the shafts is then output to the user via a user interface. 
     Another embodiment of the servo operated multi axis positioning device  80  is shown in  FIG.  15 - 17   . This simple device moves the LRF along the Y and Z axes via a servo motor relative to rotating shaft  84 . Shaft center can be determined using curve fitting as previously described or, in the simplest form, the shaft diameter and centerline height is determined by locating the top and bottom edge of the shaft. The Z distance is determined by measuring the Z location of the shaft edge and subtracting the shaft radius. The device is preferably moved along a base between four positions along the X axis by a servo to measure two shaft centerlines on each of the shafts to be aligned. 
     While exemplary embodiments are described above, it is not intended that these embodiments describe all possible forms of the invention. Rather, the words used in the specification are words of description rather than limitation, and it is understood that various changes may be made without departing from the spirit and scope of the invention. Additionally, the features of various implementing embodiments may be combined to form further embodiments of the invention.