CN103983221A - Arm changeable type joint type coordinate measuring machine - Google Patents

Abstract

The invention provides an articulated coordinate measuring machine with a variable arm, comprising: a base, a three-segment measuring arm, a rotating joint and a measuring head; The rotating joints form a space open-chain structure, and the end of the open-chain structure is the measuring head of the articulated coordinate measuring machine of the variable arm. The above-mentioned rotating joints are not locked, each joint can rotate around its own axis, the first and second level joints close to the base are fixed when the arm is changed, and the other four joints are free to move. The variable arm articulated measuring machine proposed by the invention can reduce the two angle sensors of the first stage arm and the first joint, and this structure greatly improves the measurement accuracy of the system.

Description

An Articulated Coordinate Measuring Machine With Variable Arm

technical field

The invention relates to an articulated coordinate measuring machine, in particular to an articulated coordinate measuring machine with a variable arm. the

Background technique

Articulated coordinate measuring machine is a multi-degree-of-freedom non-orthogonal coordinate measuring machine, usually with 6 degrees of freedom. It is modeled on the joint structure of the human body, and consists of three measuring arms and a measuring head connected in series through six (rotation) joints to form a space open chain structure, thereby replacing the length measurement reference with the angle measurement reference. When measuring with a measuring machine, the probe coordinates are a function of the kinematic parameters of the measuring machine and the angles of its six joints. Compared with the traditional three-coordinate measuring machine with orthogonal coordinate system, it has the advantages of large measurement range, convenience and flexibility, high precision, simple mechanical structure, and good environmental adaptability. But on the other hand, its structure is a series structure, and its various errors are transmitted to the measurement results step by step in series, so its accuracy is difficult to be guaranteed. the

Therefore, there is a need for a method of improving the measurement accuracy of an articulated coordinate measuring machine. the

Contents of the invention

The object of the present invention is to provide an articulated coordinate measuring machine with a variable arm, comprising: a base, a three-section measuring arm, six rotating joints and a measuring head, and the three-section measuring arm is connected in series on the base The rotating joints constitute a space open-chain structure, the end of which is a measuring head, and the variable-arm articulated coordinate measuring machine can realize variable-arm, full-arm and a combination of the two. In the full-arm state , the six rotating joints are not locked, and each joint can rotate around its own axis. In the state of changing arms, the first and second joints close to the base are fixed and cannot rotate, and the remaining 4 joints can rotate around It rotates on its own axis, wherein the first and second joints can be locked individually or simultaneously. the

When designing the articulated coordinate measuring machine of the variable arm, the arm length ratio optimization model is used to optimize the structural parameters. The optimization goal is to make |ΔX _T |, |ΔY _T |, |ΔZ _T | all reach the minimum value, according to the design Requirements, the following constraints exist:

① It is known that the sum of the measuring radius of the articulated coordinate measuring machine, the length of the probe l _z , and the lengths of the articulated arm d ₃ and d ₅ is a constant;

②In order to avoid measurement "fasting" area in the measurement space, it is required

③Because the variable arm articulated coordinate measuring machine adopts a double-joint integrated structure at the connection of the connecting rod, the lengths of each joint a ₁ , a ₂ , a ₃ , a ₅ , and a ₆ are 0 mm, and a ₄ has a certain length.

The arm length ratio optimization model is expressed as follows:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;X</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;Y</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;Z</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span>\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; B</span>}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}\\ <span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

The first and second joints close to the base are fixed by thread locking or pneumatic locking. the

The thread locking method is as follows: on the sleeves of the first and second joints wrapped on the outside of the rotating shaft, a locking threaded part is arranged, and the locking threaded part is screwed and protrudes toward the shaft, and leans against the shaft. This locks the hub and shaft together. the

The pneumatic locking method is as follows: the first relative rotating part and the second relative rotating part are connected through the second rotating joint, one end of the gas spring is connected to the second relative rotating part, and the other end is connected to the first relative rotating part, and the gas spring A locking handle is arranged on the spring, which can lock the two relative rotating parts of the second rotating joint at any position. the

Description of drawings

With reference to the accompanying drawings, more objects, functions and advantages of the present invention will be clarified through the following description of the embodiments of the present invention, wherein:

Fig. 1a is a coordinate system diagram of a variable arm articulated coordinate measuring machine according to the present invention. the

Fig. 1b is a schematic view of the structure of a variable-arm articulated coordinate measuring machine according to the present invention. the

Fig. 2 is a diagram of the working space of the articulated coordinate measuring machine according to the present invention. the

Fig. 3a is a schematic diagram of the thread locking method in the joint rotation locking method of the joint coordinate measuring machine according to the present invention. the

Fig. 3b is a schematic diagram of the pneumatic locking method in the joint rotation locking method of the joint coordinate measuring machine according to the present invention. the

Detailed ways

Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the drawings, the same reference numerals represent the same or similar components, or the same or similar steps. the

The present invention is described in detail in conjunction with schematic diagrams. When describing the embodiments of the present invention in detail, for the convenience of explanation, the cross-sectional view showing the structure of the device will not be partially enlarged according to the general scale, and the schematic diagram is only an example, which should not limit this invention. scope of invention protection. In addition, the three-dimensional space dimensions of length, width and depth should be included in actual production. the

Referring to Figure 1a, {O ₀ X ₀ Y ₀ Z ₀ } is the base coordinate system, {O _tp X _tp Y _tp Z _tp } is the probe coordinate system, {O _i X _i Y _i Z _i }(i=1～ 6) is the joint coordinate system established on each joint node.

In order to study the position and attitude relationship between the articulated arms, the existing mathematical models (exponential product model, DH model, improved DH model, etc.) of the articulated coordinate measuring machine were analyzed and compared. Considering the number of structural parameters of the articulated coordinate measuring machine and the orthogonality of each joint of the designed coordinate measuring machine, the commonly used DH model proposed by Denavit et al. is still used as the basis for research. There are four sets of basic structural parameters in the DH model: arm length di is the distance between adjacent X axes; joint length ai is the distance between adjacent Z axes; torsion angle αi is the angle between adjacent Z axes, It is positive if it turns left around the Xi axis; the joint rotation angle θi is the angle between adjacent X axes, and it is positive if it turns right around the Zi-1 axis. The homogeneous transformation between the joint coordinate systems is carried out by the DH method, and the coordinate system {O _i-1 X _i-1 Y _i-1 Z _i-1 } to the coordinate system {O _i X _i Y _i Z _i }( i=1～6) homogeneous transformation matrix:

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Suppose the homogeneous coordinates of probe P in the 6th joint coordinate system {O ₆ X ₆ Y ₆ Z ₆ } are X ₆ =[l ₁ , l ₂ , l ₃ , 1] ^T , in the base coordinate system {O ₀ X The homogeneous coordinates of ₀ Y ₀ Z ₀ } are p ₀ ＝[x, y , z, 1] ^T , then the probe coordinates can be expressed as:

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 6</span>}}{<span\; class="notranslate">\; \&prod;</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Formula (2) is the measurement model of the articulated coordinate measuring machine in the variable arm state, which is also applicable to the articulated coordinate measuring machine in the full arm state with six degrees of freedom. Compared with the fixed joint rotation angles θ ₁ and θ ₂ in the variable arm state, the joint rotation angles θ ₁ and θ ₂ of the articulated coordinate measuring machine in the full arm state change freely during the measurement process.

Therefore, the mathematical model of the articulated coordinate measuring machine in the full arm state includes the following parameters:

Structural parameters: ${\widehat{\mathrm{\&xi;}}}_{\mathrm{str}}=\{l_1,l_2,l_3,a_i,{\mathrm{\&alpha;}}_i,d_i\},i=1~6,$

External parameters: ${\widehat{\mathrm{\&xi;}}}_{\mathrm{ex}}=\left\{{\mathrm{\&theta;}}_i\right\},i=1~6,$

The mathematical model of the articulated coordinate measuring machine in the variable arm state after locking the first and second joints includes the following parameters:

Structural parameters: ξ _str ＝{l ₁ ,l ₂ ,l ₃ ,a _i ,α _i ,d _i ,θ ₁ ,θ ₂ }, i=1～6;

External parameters: ξ _ex ＝{θ _i }, i＝3～6.

In the actual measurement process, according to the pre-calibrated structural parameter set ξ _str and the external parameter set ξ _ex displayed by the sensor in real time, the coordinate p ₀ of the probe in the base coordinate system can be calculated according to formula (2) = [x, y, z, 1] ^T .

There are many error factors affecting the accuracy of the joint-type coordinate measuring machine, which can be divided into parameter error, environmental factor error and other factor error after research by the inventor. Parameter factor error is the most important factor causing the positioning error of the articulated coordinate measuring machine. It mainly occurs in the processing and assembly of each part in the manufacturing process, and is reflected in the four parameters in the transformation matrix between the joints. According to the structural parameter set and external parameter set established by the articulated coordinate measuring machine in the above different states, the measurement error of the probe coordinates is shown in formula (3), and the probe coordinate error of the articulated coordinate measuring machine in the full arm state is shown in formula (4 ). the

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&Delta;p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; str</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;\&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; str</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; ex</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;\&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; ex</span>}}\\ <span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;l</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;\&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; str</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}}_{\mathrm{<span\; class="notranslate">\; str</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; ex</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}}_{\mathrm{<span\; class="notranslate">\; ex</span>}}\\ <span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; l</span>}}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

The variable-arm and full-arm articulated coordinate measuring machines have the same model formula, so after system calibration, their shared structural parameters can theoretically achieve the same accuracy, namely: m=1～3; ${\mathrm{\&Delta;a}}_i={\mathrm{\&Delta;}\hat{a}}_i,{\mathrm{\&Delta;\&alpha;}}_i={\mathrm{\&Delta;}\widehat{\mathrm{\&alpha;}}}_i,{\mathrm{\&Delta;d}}_i={\mathrm{\&Delta;}\hat{d}}_i,i=1~6.$

The external parameter of the articulated coordinate measuring machine is the joint rotation angle. Due to the influence of structural design and assembly errors, the physical zero position of the angle sensor that displays the joint rotation angle and the joint zero position often do not coincide. Therefore, the error source of the joint rotation angle mainly includes the deviation between the physical zero position of the angle sensor and the joint zero position. and the indication error of the encoder. For the articulated coordinate measuring machine in the two states of variable arm and full arm, the common external parameters have the same error, namely ${\mathrm{\&Delta;\&theta;}}_i={\mathrm{\&Delta;}\widehat{\mathrm{\&theta;}}}_i,i=3~6.$

Therefore, the difference between the system measurement error of the articulated coordinate measuring machine under the state of variable arm and full arm is:

${\mathrm{<span\; class="notranslate">\; \&Delta;p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Delta;\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Delta;\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Parameter calibration can be accurate to the true value of the parameter, so the error of the structural parameters of the articulated CMM in the variable arm state after calibration is significantly smaller than the external parameter error of the articulated CMM in the full arm state that cannot be calibrated, namely therefore, According to the above analysis, the measurement error of the articulated coordinate measuring machine in the variable arm state is smaller than that of the traditional full arm state.

Analyzing the measurement model and error model of the articulated coordinate measuring machine, it can be known that its various errors are transmitted to the measurement results step by step in series, so the errors of the two angle sensors of the first-stage arm, the first and the second joint have great Accuracy has the greatest impact. the

The present invention proposes to use a variable arm articulated measuring machine to fix the first and second joints, so as to reduce the influence of the error of the two angle sensors of the first-stage arm and the first and second joints on the accuracy of the measuring machine. This structural system The measurement accuracy can be greatly improved. the

In other words, the variable arm articulated measuring machine of the present invention still retains the basic structure of the traditional articulated measuring machine with three arms and three joints (i.e. six angle sensors), but through the first and second joint locking devices, it provides Different measurement methods in the two states of variable arm and full arm: in the variable arm state, high-precision relatively small-scale measurement is performed; while in the full-arm state, low-precision relatively large-scale measurement is performed. the

In fact, according to different size measurement ranges and different accuracy requirements, the two measurement methods can also be used in combination: for the geometric parameters of the smaller size range (such as aperture and local geometry), the variable arm state is used for measurement; while the large size range , the original full-arm state is used for measurement. the

Therefore, the variable arm joint type coordinate measuring machine of the present invention can not only maintain the original performance of the measuring machine, but also achieve the purpose of high-precision measurement. At the same time, only two joint locking devices need to be added, and the cost required to improve the precision is relatively low. the

Specific embodiments of the present invention will be described below with reference to the accompanying drawings. the

Fig. 1a and Fig. 1b are schematic structural views and corresponding coordinate system diagrams of a variable arm articulated coordinate measuring machine 100 according to the present invention. the

The variable arm articulated coordinate measuring machine 100 includes: a base 110 , three measuring arms 107 , 108 , 109 , rotating joints 101 , 102 , 103 , 104 , 105 , 106 and a probe 111 . the

On the base 110, six rotatable joints 101, 102, 103, 104, 105, 106 connected in series by three sections of measuring arms 107, 108, 109 form a space open chain structure, and the end of the open chain structure is the measuring machine The measuring head 111. the

In the full-arm state, the six rotating joints 101, 102, 103, 104, 105, and 106 of the variable-arm articulated coordinate measuring machine 100 are not locked, and each joint can rotate around its own axis. The angle is controlled by a high-precision circular grating angle sensor installed on it. Due to the limitation of the mechanical structure, the joints 101, 103, 105 can rotate within the angle range of 0-2π, while the joints 102, 104, 106 can rotate within the angle range of -π-0. the

In the variable arm state, the joints 101 and 102 are locked by thread locking method and pneumatic locking method, so that they are fixed, and the remaining four joints 102, 103, 104, 105, 106 are free to move. the

The main implementation methods to make the joints rotate and lock each other are:

1. Thread locking method: as shown in Figure 3a, taking the first rotary joint 101 as an example, the shaft sleeve 301 is wrapped on the outside of the shaft part 302, and a locking threaded part 303 is arranged on the shaft sleeve 301, through the locking thread The component 303 protrudes toward the shaft and leans against the shaft, thereby locking and fixing the shaft sleeve and the shaft together. This locking method has a simple structure and is easy to use. the

2. Pneumatic locking method: as shown in Figure 3b, the first relative rotating member 308 and the second relative rotating member 304 are connected through the second rotating joint 102, one end of the gas spring 306 is connected to the second relative rotating member 304, and the other end Connected to the first relative rotating member 308 , a locking handle 307 is arranged on the gas spring 306 . In addition, the gas spring 306 is arranged on the turntable 309 , and the turntable 309 can be screwed to be fixed to the base 305 , thus realizing the locking of the first rotary joint 101 . This locking method can lock the second rotary joint 102 at any position, and the position is accurate after locking. the

In addition, after the measurement range of the articulated coordinate measuring machine is determined, the three arm lengths must be reasonably allocated. The principle of rational planning of the arm length of the articulated coordinate measuring machine is to have as large a measurement area as possible and as small a measurement blind area as possible. For the variable arm articulated coordinate measuring machine, the distribution of arm length is more scientific. Since the measurement range of the two-arm joint measuring machine is smaller than that of the three-arm joint measuring machine, in order to ensure that the general measurement needs are met, the effective measurement range should be as large as possible, so the variable arm joint type coordinate system according to the present invention The measuring machine optimizes the structural parameters of the arm length according to the following arm length proportional optimization model. the

When the measurement range of the variable-arm articulated coordinate measuring machine is determined, there are many combinations of the length parameters of each connecting rod, and the specific value of each rod parameter has an impact on the measurement range and the final probe position error. For example, the measurement radius of the measuring machine designed in an embodiment of the present invention is 1.2m, so its theoretical measurement range is a space sphere with a radius of 1.2m, that is, the origin of the probe coordinate system O ₇ X ₇ Y ₇ Z ₇ can Any point in the space sphere is detected. However, the articulated coordinate measuring machine has a working space during measurement, and the size of the working space is mainly related to d ₃ , d ₅ , α ₄ of the measuring machine and l _z of the probe, as shown in Figure 1a. If the working space can be maximized without increasing the total length of the articulated arm, reducing the inner diameter of the working area is an effective way.

The radius of the sphere in the ideal working space is d ₃ +d ₅ +l _z . From Figure 2, it can be seen that when d ₃ ≥ d ₅ , a "fasting" area A appears, and in the "fasting" area A, the probe cannot measure it. When actually designing an articulated coordinate measuring machine, there is an offset joint length α ₄ between the articulated arms d ₃ and d ₅ in order to have better rigidity and stability of the measuring machine. Therefore, when the "fasting" area appears, d ₃ , d ₅ , a ₄ , l _z have the following relationship:

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In the same way, it can be seen that when d ₃ ≤ _{d 5} , there will also be a "fasting" area, and d ₃ , d ₅ , a ₄ , l _z have the following relationship:

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

It can be seen from the above that if there is no "fasting" area in the measurement space, the relationship that d ₃ , d ₅ , a ₄ , and l _z need to satisfy is:

$<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Establish the arm length optimization model, the optimization goal is to make |ΔX _T ||ΔY _T |, |ΔZ _T | reach the minimum value, according to the design requirements, there are the following constraints:

① It is known that the sum of the measuring radius of the articulated coordinate measuring machine, the length of the probe l _z , and the lengths of the articulated arm d ₃ and d ₅ is a constant;

② In order to avoid the measurement "fasting" area in the measurement space, according to the previous research results, ${|d}_3-d_5|\&le;\sqrt{{l_z}^2-{a_4}^2}$

③As the variable arm articulated coordinate measuring machine adopts a double-joint integrated structure at the connection of the connecting rod, the joint lengths a ₁ , a ₂ , a ₃ , a ₅ , and a ₆ are 0mm, and a ₄ has a certain length.

Therefore, the arm length ratio optimization model is as follows:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;X</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;Y</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Delta;Z</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span>\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; B</span>}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}\\ <span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

It can be seen from formula (9) that the final error of the probe is not only related to θ _i , but also related to a _i and d _i of the bar parameters. In the actual measurement process, the error of the joint rotation angle variable θ _i is transmitted to the probe through the rod parameters. The arm length proportional optimization model can be applied to the arm length optimal design of the variable arm articulated coordinate measuring machine according to the present invention.

Other embodiments of the invention will be apparent to and understood by those skilled in the art from consideration of the specification and practice of the invention disclosed herein. The description and examples are considered exemplary only, with the true scope and spirit of the invention defined by the claims. the

Claims (5)

1. the articulated type coordinate measuring machine of a variable arm, comprise: pedestal, three sections of gage beams, six cradle heads and gauge head, the described cradle head Special composition open-chain structure of being connected by described three sections of gage beams on described pedestal, the end of this open-chain structure is gauge head, described variable arm articulated type coordinate measuring machine can be realized and become being used in combination of arm, full arm and both

Under full arm state, its six described cradle heads do not lock, and each joint can be rotated around the axis of himself,

Becoming under arm state, be fixed and can not rotate near the first and second joints of pedestal, all the other 4 joints can be rotated around the axis of himself,

Wherein the first and second joints can lock separately, also can lock simultaneously.

2. the articulated type coordinate measuring machine of variable arm according to claim 1, the articulated type coordinate measuring machine of wherein said variable arm adopts brachium ratio optimization model to be optimized structural parameters while design, and optimization aim is to make | Δ X _t|, | Δ Y _t|, | Δ Z _t| all reach minimum value, according to designing requirement, have following constraint condition:

1. known articulated type coordinate measuring machine is measured radius, gauge head length l _z, joint arm length d ₃, d ₅and be constant;

2. there is measuring " on an empty stomach " region, requirement for fear of measurement space

3. because variable arm articulated type coordinate measuring machine has adopted doublejointed integrative-structure in connecting rod junction, therefore each joint length a ₁, a ₂, a ₃, a ₅, a ₆for 0mm, a ₄there is certain length.

Described brachium ratio optimization model representation is as follows:

$\left\{\begin{array}{c}y=\left|\mathrm{\&Delta;}{X}_T\right|+\left|\mathrm{\&Delta;}{Y}_T\right|+\left|\mathrm{\&Delta;}{Z}_T\right|\\ d_3+d_5=A\\ a_4=B\\ a_1=a_2=a_3=a_5=a_6\\ |d_3-d_5|\&le;\sqrt{{l_z}^2-{a_4}^2}\\ d_1,d_3,d_5,a_1,a_2,a_3{,a}_4{,a}_5,a_6\&GreaterEqual;0\end{array}\right....\left(1\right).$

3. the articulated type coordinate measuring machine of variable arm according to claim 1, is wherein fixed by thread lock or Pneumatic locking mode near the first and second joints of pedestal.

4. the articulated type coordinate measuring machine of variable arm according to claim 1, wherein said thread lock mode is: on the axle sleeve that wraps in rotating shaft outside in first and second joint, be furnished with locking screw parts, screw and to axial region projection by locking screw parts, be resisted against axial region, thereby axle sleeve and axial region are locked together.

5. the articulated type coordinate measuring machine of variable arm according to claim 1, wherein said pneuma-lock mode is: first-phase is connected by the second cradle head to tumbler with second-phase to tumbler, gas spring one end is connected to second-phase to tumbler, the other end is connected to first-phase on tumbler, on gas spring, be furnished with set lever, two that can lock at an arbitrary position the second cradle head relatively rotate part.