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

Abstract

The invention provides an arm changeable type joint type coordinate measuring machine. The arm changeable type joint type coordinate measuring machine comprises a base, three measuring arms, rotational joints and a measuring head. On the base, a space open chain structure is formed by the six rotational joints serially connected by the three measuring arms. The tail end of the open chain structure is provided with the measuring head of the arm changeable type joint type coordinate measuring machine. According to the arm changeable type joint type coordinate measuring machine, in the full arm state, the six rotational joints do not be locked, and each joint can be rotated around the axis of itself, and in the arm changeable state, the first and second joints which are close to the base are fixed, and other four joints can be moved freely. The arm changeable type joint type measuring machine provided in the invention can be used to reduce two angle sensors of the first arm and the first joint, and through the structure, the system measuring accuracy can be greatly improved.

Description

A kind of articulated type coordinate measuring machine of variable arm

Technical field

The present invention relates to articulated type coordinate measuring machine, be specifically related to a kind of articulated type coordinate measuring machine of variable arm.

Background technology

Articulated type coordinate measuring machine is the three coordinate measuring machine of the nonopiate co-ordinate-type of a kind of multiple degrees of freedom, conventionally has 6 degree of freedom.It copies human synovial structure, is connected in series Special composition open-chain structure, thereby has replaced linear measure longimetry benchmark with measurement of angle benchmark by three gage beams and a gauge head by six (rotation) joints.In the time using measuring machine to measure, gauge head coordinate is the function of measuring machine kinematics parameters and its six joint angles.Compared with traditional orthogonal coordinate system formula three coordinate measuring machine, the advantages such as measurement range is large, convenient, flexible, precision is higher, physical construction is simple, good environmental adaptability that it has.But its structure is a kind of cascaded structure on the other hand, its every error is that tandem is delivered to measurement result step by step, thereby its precision is difficult to be guaranteed.

Therefore, need a kind of method of the measuring accuracy that improves articulated type coordinate measuring machine.

Summary of the invention

The object of this invention is to provide a kind of articulated type coordinate measuring machine of 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 change arm, full arm and both are used in combination, under full arm state, its six described cradle heads do not lock, each joint can be rotated around the axis of himself, becoming under arm state, the first and second joints near pedestal are fixed and can not rotate, 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.

The articulated type coordinate measuring machine of described 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:

$\left\{\begin{array}{c}y=\left|{\mathrm{\ΔX}}_T\right|+\left|{\mathrm{\ΔY}}_T\right|+\left|{\mathrm{\ΔZ}}_T\right|\\ d_3+d_5=A\\ a_4=B\\ a_1=a_2=a_3=a_5=a_6\\ |d_3-d_5|\≤\sqrt{{l_z}^2-{a_4}^2}\\ d_1,d_3,d_5,a_1,a_2,a_3,a_4,a_5,a_6\≥0\end{array}\right....\left(1\right).$

Described the first and second joints near pedestal are fixed by thread lock or Pneumatic locking mode.

Described 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, screwed and to axial region projection, be resisted against axial region, thereby axle sleeve and axial region are locked together by locking screw parts.

Described 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.

Brief description of the drawings

With reference to the accompanying drawing of enclosing, the more object of the present invention, function and advantage are illustrated the following description by embodiment of the present invention, wherein:

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

Fig. 1 b is according to the structural outline view of variable arm articulated type coordinate measuring machine of the present invention.

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

Fig. 3 a is according to the schematic diagram of the screw-threaded coupling method in the method for the mutual twist-lock in joint of joint coordinates measuring machine of the present invention.

Fig. 3 b is according to the schematic diagram of the pneuma-lock method in the method for the mutual twist-lock in joint of joint coordinates measuring machine of the present invention.

Embodiment

Hereinafter, embodiments of the invention will be described with reference to the drawings.In the accompanying drawings, identical Reference numeral represents same or similar parts, or same or similar step.

Be described in detail in conjunction with schematic diagram for the present invention; in the time that the embodiment of the present invention is described in detail in detail, for ease of explanation, represent that the sectional view of device architecture can be disobeyed local amplification of general ratio work; and described schematic diagram is example, it should not limit the scope of protection of the invention at this.In addition in actual fabrication, should comprise, the three-dimensional space of length, width and the degree of depth.

Referring to Fig. 1 a, { O ₀x ₀y ₀z ₀be basis coordinates system, { O _tpx _tpy _tpz _tpbe gauge head coordinate system, { O _ix _iy _iz _i(i=1～6) joint coordinate system for setting up on the node of each joint.

In order to study position and the attitude relation between each joint arm, the existing mathematical model (exponent product model, D-H model, improved D-H model etc.) of articulated type coordinate measuring machine is carried out to correlation analysis comparison.In the situation that considering that articulated type coordinate measuring machine structural parameters number and the each joint of designed coordinate measuring machine are orthogonal, still select the D-H model of the propositions such as conventional Denavit for launching research in basis.In D-H model, there are four groups of elementary structure parameters: brachium di is the distance between adjacent X-axis; Joint length ai is the distance between adjacent Z axis; Torsion angle α i is the angle between adjacent Z axis, with left-handed for just around Xi axle; Joint rotation angle θ i is the angle between adjacent X-axis, with around the dextrorotation of Zi-1 axle for just.Carry out the homogeneous transformation between joint coordinate system by D-H method, just can obtain coordinate system { O _i-1x _i-1y _i-1z _i-1to coordinate system { O _ix _iy _iz _ithe homogeneous transformation matrix of (i=1～6):

$T_{i-1,i}=\left[\begin{array}{cccc}\cos {\mathrm{\θ}}_i& -\sin {\mathrm{\θ}}_i\cos {\mathrm{\α}}_i& \sin {\mathrm{\θ}}_i\sin {\mathrm{\α}}_i& {\mathrm{\α}}_i\cos {\mathrm{\θ}}_i\\ \sin {\mathrm{\θ}}_i& \cos {\mathrm{\θ}}_i\cos {\mathrm{\α}}_i& -\cos {\mathrm{\θ}}_i\sin {\mathrm{\α}}_i& {\mathrm{\α}}_i\sin {\mathrm{\θ}}_i\\ 0& \sin {\mathrm{\α}}_i& \cos {\mathrm{\α}}_i& d_i\\ 0& 0& 0& 0\end{array}\right]...\left(1\right)$

Suppose that gauge head P is at the 6th joint coordinate system { O ₆x ₆y ₆z ₆homogeneous coordinates be X ₆=[l ₁, l ₂, l ₃, 1] ^t, at { the O of basis coordinates system ₀x ₀y ₀z ₀homogeneous coordinates be p ₀=[x, y, z, 1] ^t, gauge head coordinate can be expressed as so:

$p_0=\left(\underset{i=1}{\overset{6}{\∏}}{T}_{i-1,i}\right)X_6...\left(2\right)$

Formula (2) is exactly the measurement model that becomes the articulated type coordinate measuring machine of arm state, and it is equally applicable to the articulated type coordinate measuring machine of the full arm state of six degree of freedom.With fixing joint rotational angle theta under change arm state ₁and θ ₂compare the joint rotation angle θ of the articulated type coordinate measuring machine of full arm state ₁and θ ₂in measuring process, freely change.

Therefore, the mathematical model of the articulated type coordinate measuring machine of full arm state comprises following parameter:

Structural parameters: ${\widehat{\mathrm{\ξ}}}_{\mathrm{str}}=\{l_1,l_2,l_3,a_i,{\mathrm{\α}}_i,d_i\},i=1~6,$

External parameter: ${\widehat{\mathrm{\ξ}}}_{\mathrm{ex}}=\left\{{\mathrm{\θ}}_i\right\},i=1~6,$

The mathematical model that locks the articulated type coordinate measuring machine of the 1st and the 2nd postarticular change arm state comprises following parameter:

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

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

The structural parameters collection ξ that basis is demarcated in advance in actual measurement process _strwith the sensor external parameter collection ξ of demonstration in real time _ex, can calculate the coordinate p of gauge head under basis coordinates system according to formula (2) ₀=[x, y, z, 1] ^t.

The error component that affects articulated type coordinate measuring machine accuracy is numerous, can be divided into parameter factor error, environmental factor error, other factors error through inventor's research.Parameter factor error is to cause the main factor of articulated type coordinate measuring machine positioning error, mainly results from processing and the assembling of the each parts of manufacture process, in four parameters of concentrated reflection in the internode transformation matrix of each pass.Structural parameters collection and the external parameter collection set up according to above-mentioned different conditions hypozygal formula coordinate measuring machine, the measuring error of gauge head coordinate is shown in formula (3), and the gauge head error of coordinate of the articulated type coordinate measuring machine of full arm state is shown in formula (4).

$\begin{array}{c}{\mathrm{\Δp}}_0=\left|\frac{{\∂p}_0}{{\∂\mathrm{\ξ}}_{\mathrm{str}}}\right|{\mathrm{\Δ\ξ}}_{\mathrm{str}}+\left|\frac{{\∂p}_0}{{\∂\mathrm{\ξ}}_{\mathrm{ex}}}\right|{\mathrm{\Δ\ξ}}_{\mathrm{ex}}\\ =\left[\underset{i=1}{\overset{2}{\mathrm{\Σ}}}\right|\frac{{\∂p}_0}{{\∂\mathrm{\θ}}_i}|{\mathrm{\Δ\θ}}_i+\underset{m=1}{\overset{3}{\mathrm{\Σ}}}|\frac{{\∂p}_0}{{\∂l}_m}|{\mathrm{\Δl}}_m+\underset{i=1}{\overset{6}{\mathrm{\Σ}}}\left(\right|\frac{{\∂p}_0}{{\∂a}_i}|{\mathrm{\Δa}}_i+|\frac{{\∂p}_0}{{\∂\mathrm{\α}}_i}|{\mathrm{\Δ\α}}_i+|\frac{{\∂p}_0}{{\∂d}_i}\left|{\mathrm{\Δd}}_i\right)]+\left[\underset{i=3}{\overset{6}{\mathrm{\Σ}}}\right|\frac{{\∂p}_0}{{\∂\mathrm{\θ}}_i}|{\mathrm{\Δ\θ}}_i\end{array}...\left(3\right)$

$\begin{array}{c}{\mathrm{\Δ}\hat{p}}_0=\left|\frac{{\∂p}_0}{{\∂\mathrm{\ξ}}_{\mathrm{str}}}\right|{\mathrm{\Δ}\widehat{\mathrm{\ξ}}}_{\mathrm{str}}+\left|\frac{{\∂p}_0}{{\∂\mathrm{\ξ}}_{\mathrm{ex}}}\right|{\mathrm{\Δ}\widehat{\mathrm{\ξ}}}_{\mathrm{ex}}\\ =\left[\underset{m=1}{\overset{3}{\mathrm{\Σ}}}\right|\frac{{\∂p}_0}{{\∂l}_m}|{\mathrm{\Δ}\hat{l}}_m+\underset{i=1}{\overset{6}{\mathrm{\Σ}}}\left(\right|\frac{{\∂p}_0}{{\∂a}_i}|\mathrm{\Δ}{\hat{a}}_i+|\frac{{\∂p}_0}{{\∂\mathrm{\α}}_i}|{\mathrm{\Δ}\widehat{\mathrm{\α}}}_i+|\frac{{\∂p}_0}{{\∂d}_i}\left|{\mathrm{\Δ}\hat{d}}_i\right)]+\left[\underset{i=1}{\overset{6}{\mathrm{\Σ}}}\right|\frac{{\∂p}_0}{{\∂\mathrm{\θ}}_i}|{\mathrm{\Δ}\widehat{\mathrm{\θ}}}_i\end{array}...\left(4\right)$

Become arm and have identical model formation with full arm two class articulated type coordinate measuring machines, therefore, by after system calibrating, its total structural parameters can reach identical precision in theory, that is: m=1～3; ${\mathrm{\Δa}}_i={\mathrm{\Δ}\hat{a}}_i,{\mathrm{\Δ\α}}_i={\mathrm{\Δ}\widehat{\mathrm{\α}}}_i,{\mathrm{\Δd}}_i={\mathrm{\Δ}\hat{d}}_i,i=1~6.$

The external parameter of articulated type coordinate measuring machine is joint rotation angle.Due to the impact of structural design and rigging error, the angular transducer physics zero-bit that shows joint rotation angle tends to not overlap with joint zero-bit, therefore, the source of error of joint rotation angle mainly comprises the deviation between angular transducer physics zero-bit and joint zero-bit, and the index error of scrambler.For the articulated type coordinate measuring machine becoming under arm and full arm two states, its total external parameter has identical error, ${\mathrm{\Δ\θ}}_i={\mathrm{\Δ}\widehat{\mathrm{\θ}}}_i,i=3~6.$

Therefore, the difference of the systematic measurement error of the articulated type coordinate measuring machine under change arm and full arm state is:

${\mathrm{\Δp}}_0-{\mathrm{\Δ}\hat{p}}_0=\left|\frac{{\∂p}_0}{{\∂\mathrm{\θ}}_1}\right|({\mathrm{\Δ\θ}}_1-{\mathrm{\Δ}\widehat{\mathrm{\θ}}}_1)+\left|\frac{{\∂p}_0}{{\∂\mathrm{\θ}}_2}\right|({\mathrm{\Δ\θ}}_2-{\mathrm{\Δ}\widehat{\mathrm{\θ}}}_2)...\left(5\right)$

Parameter calibration can accurate parameters true value, and therefore the error of the articulated type coordinate measuring machine structural parameters under calibrated change arm state is significantly less than the external parameter error of the articulated type coordinate measuring machine under the full arm state that cannot demarcate, therefore, according to above-mentioned analysis, the measuring error that becomes the articulated type coordinate measuring machine under arm state is less than the measuring error of the articulated type coordinate measuring machine under traditional full arm state.

Measurement model and the error model of analysis of joint formula coordinate measuring machine are known, and its every error is that tandem is delivered to measurement result step by step, and therefore two angular transducer errors in first order arm, the first and second joints are to measuring machine Accuracy maximum.

The present invention proposes to adopt variable arm articulated type measuring machine, fixes the first and second joints, the impact with two angular transducer errors reducing first order arm and the first and second joints on measuring machine precision, and the measuring accuracy of this structural system can improve greatly.

In other words, variable arm articulated type measuring machine of the present invention still retains the basic structure of original three arms of traditional articulated type measuring machine and three joints (i.e. six angular transducers), but by the first and second joint locking devices, provide in the different measuring mode becoming under arm and full arm two states: becoming under arm state, carrying out the relative range of small of high precision and measure; And under full arm state, carry out the relative large-scale metrology of low precision.

In fact, according to different size measurement range and different accuracy requirement, two kinds of measuring methods also can be used in combination: for the geometric parameter (as aperture and local geometric configuration) of smaller size range, adopt change arm state to measure; And large scale scope adopts original full arm state to measure.

Therefore variable arm articulated type coordinate measuring machine of the present invention both can keep the original performance of measuring machine, can reach again high-acruracy survey object, only need to increase by two joint locking devices simultaneously, improved the required cost of precision lower.

Below with reference to accompanying drawing, the specific embodiment of the present invention is described.

Fig. 1 a and Fig. 1 b are according to the structural outline view of variable arm articulated type coordinate measuring machine 100 of the present invention and corresponding coordinate system figure thereof.

Described variable arm articulated type coordinate measuring machine 100 comprises: 110, three sections of gage beams of pedestal 107,108,109, cradle head 101,102,103,104,105,106 and gauge head 111.

On pedestal 110, by six rotatable joint 101,102,103,104,105,106 Special composition open-chain structures of three sections of gage beams, 107,108,109 series connection, the end of this open-chain structure is the gauge head 111 of measuring machine.

Under full arm state, six cradle heads 101,102,103,104,105,106 of described variable arm articulated type coordinate measuring machine 100 do not lock, each joint can be rotated around the axis of himself, and the angle that rotate in joint is obtained by the high accuracy circular Grating Angle Sensor control of installing on it.Due to physical construction restriction, wherein joint 101,103,105 can rotate in 0～2 π angular range, and joint 102,104,106 can rotate in-π～0 angular range.

Becoming under arm state, joint 101 and joint 102 are locked by screw-threaded coupling method, pneuma-lock method, make it to maintain static, and all the other 4 joints 102,103,104,105,106 can be freely movable.

The main implementation method of the mutual twist-lock in joint is had:

1. screw-threaded coupling method: as shown in Figure 3 a, taking the first cradle head 101 as example, axle sleeve 301 wraps in the outside of axial region 302, on axle sleeve 301, be furnished with locking screw parts 303, to axial region projection, be resisted against axial region by locking screw parts 303, thereby by axle sleeve with axial region is locked is fixed together, this locking method is simple in structure, easy to use.

2. pneuma-lock method: as shown in Figure 3 b, first-phase is connected by the second cradle head 102 to tumbler 304 with second-phase to tumbler 308, gas spring 306 one end are connected to second-phase to tumbler 304, the other end is connected to first-phase on tumbler 308, is furnished with set lever 307 on gas spring 306.In addition, gas spring 306 is arranged on rotating disk 309, and rotating disk 309 can be fixed to base 305 by thread lock again, has realized so again the locking of the first cradle head 101.This locking method can be locked the second cradle head 102 at an arbitrary position, and after locking, position is accurate.

In addition, articulated type coordinate measuring machine is after the measurement range of measuring machine is determined, three brachiums must reasonable distribution.The principle that articulated type coordinate measuring machine brachium is made rational planning for is, should have large as far as possible measured zone, has again as far as possible little measurement blind area.For variable arm articulated type coordinate measuring machine, its brachium distribution has more its scientific meaning.Because the measurement range of two shoulder joint measuring machines reduces to some extent than the measurement range of three shoulder joint measuring machines, in order to ensure to adapt to general measure needs, should have the large effective range of trying one's best, therefore variable arm articulated type coordinate measuring machine according to the present invention is optimized brachium structural parameters according to following brachium ratio optimization model.

In the case of the measurement range of variable arm articulated type coordinate measuring machine is definite, each length of connecting rod parameter has multiple combination, and the concrete value of each rod member parameter has impact to measurement range and final probe location error.For example, the measurement radius of the measuring machine of one embodiment of the present of invention design is 1.2m, and therefore its theoretical measurement range is that radius is the space spheroid of 1.2m, i.e. gauge head coordinate system O ₇x ₇y ₇z ₇initial point can detect any point in the spheroid of space.But there is work space in articulated type coordinate measuring machine in the time measuring, the d of the main and measuring machine of work space size ₃, d ₅, α ₄and the l of gauge head _zrelevant, as shown in Figure 1a.If make its work space reach maximum under the prerequisite that does not increase joint arm overall length, the internal diameter that reduces operation interval is an effective way.

The radius of ideal operation space spheroid is d ₃+ d ₅+ l _z, work as can be seen from Figure 2 d ₃>=d ₅time occur " on an empty stomach " region A, in " on an empty stomach " region A, gauge head cannot measure.In the time of actual design articulated type coordinate measuring machine, for measuring machine can have better rigidity and stability, at joint arm d ₃, d ₅between also have biasing joint length α ₄.Therefore occurring when " on an empty stomach " region, d ₃, d ₅, a ₄, l _zthere is following relation:

$d_5\≤d_3-\sqrt{{l_z}^2-{a_4}^2}---\left(6\right)$

In like manner known, work as d ₃≤ d ₅also there will be " on an empty stomach " region, d ₃, d ₅, a ₄, l _zthere is following relation:

$d_5\≥d_3+\sqrt{{l_z}^2-{a_4}^2}---\left(7\right)$

As from the foregoing, if not there is not " on an empty stomach " region, d in measurement space ₃, d ₅, a ₄, l _zneed satisfied pass to be:

$|d_3-d_5|\≤\sqrt{{l_z}^2-{a_4}^2}---\left(8\right)$

Set up brachium Optimized model, 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. occur measuring " on an empty stomach " region for fear of measurement space, known according to result of study above, ${|d}_3-d_5|\≤\sqrt{{l_z}^2-{a_4}^2}$

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

Therefore, brachium ratio optimization model is as follows:

$\left\{\begin{array}{c}y=\left|{\mathrm{\ΔX}}_T\right|+\left|{\mathrm{\ΔY}}_T\right|+\left|{\mathrm{\ΔZ}}_T\right|\\ d_3+d_5=A\\ a_4=B\\ a_1=a_2=a_3=a_5=a_6\\ |d_3-d_5|\≤\sqrt{{l_z}^2-{a_4}^2}\\ d_1,d_3,d_5,a_1,a_2,a_3,a_4,a_5,a_6\≥0\end{array}\right....\left(9\right)$

Known by formula (9), the final error of gauge head not only with θ _irelevant, also with a of rod member parameter _i, d _irelevant.In actual measuring process, joint rotation angle variable θ _ierror be delivered to gauge head by rod member parameter exactly.This brachium ratio optimization model can be applied to according to the brachium optimal design of variable arm articulated type coordinate measuring machine of the present invention.

In conjunction with the explanation of the present invention and the practice that disclose here, other embodiment of the present invention are easy to expect and understand for those skilled in the art.Illustrate with embodiment and be only considered to exemplary, true scope of the present invention and purport limit by claim.

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:

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

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.