Kinematic Calibration

Laser Tracker error modeling and kinematic calibration strategy... 

Keywords Laser Tracker, kinematic calibration, synthetic data. 

R. Furutani, K. Shimojima, K. Takamasu, Kinematical calibration of articulated CMM using multiple simple artifacts, XVIIIMEKO World Congress, (2003) 1798-1801. 

L.J. Everett, C.Y. Lin, Kinematic Calibration of Manipulators with Closed Loop Actuated Joints, Proceedings of the IEEE International Conference on Robotics and Automation, Philadelphia, PA, USA, 1988, pp. 792-797. 

P. Renaud, N. Andreff, J.M. Lavest, M. Dhome, Simplifying the Kinematic Calibration of Parallel Mechanisms using Vision-Based Metrology, leee Transactions on Robotics, 22 (2006) 12-22. 

A. Majarena, J. Santolaria, D. Samper, J. Aguilar, Analysis and Evaluation of Objective Functions in Kinematic Calibration of Parallel Mechanisms, The International Journal of Advanced Manufacturing Technology, (2013) 1-11. 

Calibrate the GMF robot using the generic forward kinematic calibration software developed at Texas A M University. 

This is the essential characteristic for every lubricant. The kinematic viscosity is most often measured by recording the time needed for the oil to flow down a calibrated capillary tube. The viscosity varies with the pressure but the influence of temperature is much greater it decreases rapidly with an increase in temperature and there is abundant literature concerning the equations and graphs relating these two parameters. One can cite in particular the ASTM D 341 standard. 

The viscosity is determined by measuring the time it takes for a crude to flow through a capillary tube of a given length at a precise temperature. This is called the kinematic viscosity, expressed in mm /s. It is defined by the standards, NF T 60-100 or ASTM D 445. Viscosity can also be determined by measuring the time it takes for the oil to flow through a calibrated orifice standard ASTM D 88. It is expressed in Saybolt seconds (SSU). 

In the SI system, the theoretical unit of v is m2/s or the commonly used Stoke (St) where 1 St = 0.0001 m2/s = 100 cSt = 100 centiStoke. Similarly, 1 centiStoke = 1 cSt = 0.000001 m2/s = 0.01 Stoke = 0.01 st. The specific gravity of water at 20.2°C (68.4°F) is almost 1. The kinematic viscosity of water at 20.2°C (68.4°F) is for all practical purposes equal to 1 cSt. For a liquid, the kinematic viscosity will decrease with higher temperature. For a gas, the kinematic viscosity will increase with higher temperature. Another commonly used kinematic viscosity unit is Saybolt universal seconds (SUS), which is the efflux time required for 60 mL of petroleum product to flow through the calibrated orifice of a Saybolt universal viscometer, as described by ASTM-D88. Therefore, the relationship between dynamic viscosity and kinematic viscosity can be expressed as... 

Saybolt Universal Seconds (SUS) are used to measure viscosity. The efflux time is the SUS required for 60 mL of a petroleum product to flow through the calibrated orifice of a Saybolt Universal viscometer, under carefully controlled temperature and as prescribed by test method ASTM D 88. This method has largely been replaced by the kinematic viscosity method. SUS is also called the SSU number (Seconds Saybolt Universal) or SSF number (Saybolt Seconds Furol). 

The side-by-side diffusion cell has also been calibrated for drug delivery mass transport studies using polymeric membranes [12], The mass transport coefficient, D/h, was evaluated with diffusion data for benzoic acid in aqueous solutions of polyethylene glycol 400 at 37°C. By varying the polyethylene glycol 400 content incrementally from 0 to 40%, the kinematic viscosity of the diffusion medium, saturation solubility for benzoic acid, and diffusivity of benzoic acid could be varied. The resulting mass transport coefficients, D/h, were correlated with the Sherwood number (Sh), Reynolds number (Re), and Schmidt number (Sc) according to the relationships... 

In order to calculate the kinematic viscosity, the calibration constant for the viscometer in question must be known. This calibration constant is often determined by the vendor before it is shipped, but it is also often checked by the user. In the calibration procedure, a fluid of known viscosity is tested so that the calibration constant can then be calculated ... 

A given calibration liquid is known to have a kinematic viscosity of 15.61 cS at 25°C. Testing this liquid in a capillary viscometer gave a time of 139 sec. An unknown liquid was then tested with the same viscometer and found to give a time of 238 sec. What is the kinematic viscosity of the unknown liquid ... 

Pour the first liquid to be measured into the viscometer tube and place the tube in the constant temperature bath. After allowing plenty of time for the temperature to equilibrate, measure the time of flow in the manner discussed in Section 15.2.4. Using the known calibration constant, calculate the kinematic viscosity at 25°C. Repeat with each of the other alcohols. 

The Saybolt universal viscosity equivalent to a given kinematic viscosity varies slightly with the temperature at which the determination is made because the temperature of the calibrated receiving flask used in the Saybolt method is not the same as that of the oil. Conversion factors are used to convert kinematic viscosity from 2 to 70 cSt at 38°C (100°F) and 99°C (210°F) to equivalent Saybolt universal viscosity in seconds. Appropriate multipliers are listed to convert kinematic viscosity over 70 cSt. For a kinematic viscosity determined at any other temperature, the equivalent Saybolt universal value is calculated by use of the Saybolt equivalent at 38°C (100°F) and a multiplier that varies with the temperature ... 

If it is necessary to calculate kinematic viscosities from efflux times, such as in a calibration procedure, equation 20 should be used, where /is the efflux time and k and K are constants characteristic of the particular viscosity cup (see Table 5) (158,159). 

Linear equations of the type v = ct — C, where c and C are constants, relate kinematic viscosity to efflux time over limited time ranges. This is based on the fact that, for many viscometers, portions of the viscosity—time curves can be taken as straight lines over moderate time ranges. Linear equations, which are simpler to use in determining and applying correction factors after calibration, must be applied carefully as they do not represent the true viscosity—time relation. Linear equation constants have been given (158) and are used in ASTM D4212. 

The Saybolt universal viscosity (SUS) equivalent to a given kinematic viscosity varies slightly with the temperature at which the determination is made because the temperature of the calibrated receiving flask used in the Saybolt method is not the same as that of the oil. Conversion factors are used to convert... 

Viscosity. It shall be detd in accordance with method 305.6 of Federal Test Method Std 791B (Jan 1969) (ASTM Method D445-65). The time is measured for a fixed vol of the liq to flow thru a calibtated Ubbelohde capillary viscometer under an accurately reproducible head and at a closely controlled temp. The kinetic viscosity is then calculated from the measured time flow and the calibration constant of the viscometer. Kinetic viscosity is a measure of the time for a fixed vol of liq to flow by gravity thru a capillary. It is usually expressed in centistokes, cSt, so that 1 St = 100 cSt. The dynamic viscosity is the product of kinematic viscosity density of the liq, both at same temp. The unit is poise, P, in g/cm/sec [For details see ASTM Standard, Part 17(1971), ppl78—83]... 

In the test, the time for a fixed volume of liquid to flow under gravity through the capillary of a calibrated viscometer under a reproducible driving head and at a closely controlled temperature is measured in seconds. The kinematic viscosity is the product of the measured flow time and the calibration constant of the viscometer. Conversion of the kinematic viscosity in centistokes (cSt) at any temperature to Saybolt Universal viscosity in Saybolt Universal seconds (SUS) at the same temperature and for converting kinematic viscosity in centistokes at 122 and 210°F to Saybolt Furol viscosity in Saybolt Furol seconds (SFS) at the same temperatures (ASTM D-2161) is avaibale through formulae. 

The use of these empirical procedures is being superseded by the more precise kinematic viscosity method (ASTM D-445, IP 71), in which a fixed volume of fuel flows through the capillary of a calibrated glass capillary viscometer under an accurately reproducible head and at a closely controlled temperature. The result is obtained from the product of the time taken for the fuel to flow between two etched marks on the capillary tube and the calibration factor of the viscometer and is reported in centistokes. Because the viscosity decreases with increasing temperature the temperature of test must also be reported if the viscosity value is to have any significance. For distillate fuel oils the usual test temperature is 38°C (100°F). 

Kinematic viscosity is measured by timing the flow of a fixed volume of material through a calibrated capillary at a selected temperature (ASTM D-445, IP 71). The unit of kinematic viscosity is the stokes, and kinematic viscosities of waxes are usually reported in centistokes. Saybolt Universal seconds can be derived from centistokes (ASTM D-2161) ... 

The great advantage of crystal analyser spectrometers is that there are no moving parts in the spectrometer. Even physically moving the instrument is not problematic because TOSCA uses a kinematic mount system and the whole spectrometer can be removed and replaced within a day but the calibration remains unaltered. An advantage of this feature is that the conversion to S(Q,co) can be initiated automatically when the current spectrum has finished accumulating, with fiill confidence in the... 

The most common viscosity test is the kinematic viscosity method (ASTM D445, IP-71, DIN 51566 and ISO 3104). Note that lubricant viscosity is discussed in detail in the next chapter. The kinematic viscosity is the product of the time of flow and the calibration factor of the instrument. The test determines the kinematic viscosity of liquid lubricants by measuring the time taken for a specific volume of the liquid to flow through a calibrated glass capillary viscometer under specified driving head (gravity) and temperature conditions. The test is usually performed at a lubricant temperature of 40°C and/or 100°C to standardize the results obtained and allow comparison among different users. 

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