the present invention provides a three - link toggle type positioning platform . for complete understanding of the present invention , the following description will describe in detail the method steps and the components . the present invention is not limited by the specified particulars of the radiation emitting semiconductor devices that are familiar to persons skilled in the art . in addition , well - known components or method steps are not described in detail so as to avoid any additional limitation . the preferable embodiments of the present invention are described in detail . in addition to the detailed descriptions , the present invention also can be applied to other embodiments . therefore , the scope of the present invention is not limited , and is dependent on the following claims . the present invention is based on a three - link theorem which is shown by a schematic diagram of a three - link structure in fig2 . according to the diagram , we can substitute each angle and distance into two trigonometric equations below . 4 a × sin ( θ 2 )− b × cos ( θ 3 )= 73 . 87 + c ( 1 ) b × sin ( θ 3 )− 4 a × cos ( θ 2 )= d ( 2 ) then by applying pythagorean theorem , the above equation can be converted as : b × sin ( θ 3 )=( b 2 −( 4 a × sin ( θ 2 )− c ) 2 ) 1 / 2 by substituting the above equation into equation ( 2 ), the following equation can be obtained . ( b 2 −( 4 a × sin ( θ 2 )− c ) 2 ) 0 . 5 − 4 a × cos ( θ 2 )− d = 0 ( 3 ) a × sin ( θ 2 )+ b × cos ( θ 4 )= c ( 4 ) then by applying pythagorean theorem , the above equation can be converted as : by substituting the above equation into equation ( 5 ), the following equation can be obtained . a × cos ( θ 2 )−( b 2 −( c − a × sin ( θ 2 ) 2 ) 1 / 2 )−( d + 106 . 9445 )= 0 ( 6 ) where parameter a , b , c , d , b , c , θ 2 , θ 3 and θ 4 are clearly shown in fig2 , where a moving distance of platform d and a number of turns of motor c are unknown , and the following equation ( 7 ) and ( 8 ) can be obtained by substituting the above parameters into equation ( 3 ) and ( 6 ). then utilizing a software called matlab to calculate equation ( 7 ) and ( 8 ). since the known angel θ 2 is 90 °, according to fig1 , the moving distance of platform d can be obtained by substituting the number of turns of motor c into equation ( 7 ) and ( 8 ). fig3 is a theoretical curve diagram showing a relation between the number of turns of motor and the moving distance of platform , wherein the number of turns of motor and the moving distance of platform are in direct proportion , that is to say , when the number of turns of motor increases , the moving distance of platform will increase , too . further , a slope value of the theoretical curve is large in the beginning . however , when the motor reached 98 turns , the moving distance of platform is significantly slowing down , thereby decreasing the slope value of the theoretical curve . in other words , according to the theoretical value , the present invention not only increases the moving speed of the platform but also improves the precision thereof . fig4 is a top view showing a three - link toggle type positioning platform of the present invention . according to one embodiment , the present invention discloses a three - link toggle type positioning platform 10 which comprises a first platform 12 , a first motor 46 , a first ballscrew 32 , a second platform 14 , a first linkage 34 , a second linkage 36 and a third linkage 38 . the first motor 46 is disposed on the first platform 12 . the first ballscrew 32 is disposed on the first platform 12 and coupled to the first motor 46 , wherein the first motor 46 is suitable for driving the first ballscrew 32 to rotate . the second platform 14 is disposed on the first platform 12 , wherein the second platform 14 is suitable for moving back and fourth alternately along a first predetermined path 54 , wherein a first angle 22 is existed between an extended direction of the first predetermined path 54 and the first ballscrew 32 . the second linkage 36 is fixed on a first base 48 , and is parallel to the first ballscrew 32 and the second platform 14 . the first linkage 34 is disposed between the first ballscrew 32 and the second linkage 36 , wherein a second angle 24 existed between the first ballscrew 32 and the first linkage 34 . the third linkage 38 is disposed between the second linkage 36 and the second platform 14 , wherein a third angle 26 is existed between the second linkae 36 and the third linkage 38 . moreover , the first linkage 34 , the second linkage 36 and the third linkage 38 are driven simultaneously by the rotation of the first ballscrew 32 , such that the second platform 14 is driven to move along the first predetermined path 54 . further , fig5 shows a solid diagram of a three - link toggle type positioning platform according to the present invention . the aforesaid second platform 14 can move back and fourth along the first predetermined path 54 with the help of a first linear bearing 44 and a first slide rail 42 . the present invention comprises a first linear bearing 44 penetrates a first slide rail 42 , wherein two opposite ends of the first slide rail 42 are fixed on respective supporting frames 50 . the length of the first slide rail 42 is equal to that of the first predetermined path 54 . the moving direction of the first linear bearing 44 and the first slide rail 42 is perpendicular to the first ballscrew 32 . furthermore , the first linear bearing 44 and the first slide rail 42 are disposed between the first platform 12 and the second platform 14 and fixed on two opposite sides of the third platform 14 . due to the first linear bearing 44 is a long - shaped cylindrical tube , which is made of iron or other material , the second platform 14 can not being fixed on it . in the present embodiment , the first linear bearing 44 is fixed in a stable long - shaped quadrate tube in order to form a flat surface which disposed between the second platform 14 and the third platform 70 to avoid roatation . the second platform 14 may have a guide groove and the third platform 70 is suitable for moving along the guide groove . the guide groove has a cross - section of v - shape , u - shape , or other shapes . besides , the present embodiment further comprises a ball bearing . the ball bearing is disposed on the second platform 14 and is between the second platform 14 and the third platform 70 , and therefore the second platform 14 may move along the first predetermined path 54 . in brief , the ball bearing may move along the guide groove ( not shown ). the connecting structure for three - link linkage is to connect two opposite ends of the first linkage 34 with the first ballscrew 32 and the second linkage 36 , and a second angle 24 is existed between the first ballscrew 32 and the fisrdt linkage 34 . one opposite end of the second linkage 36 is fixed on the first base 48 , wherein the first base 48 can support the second linkage 36 . one end of the third linkage 38 connects to the second linkage 36 where near the first base 48 . moreover , one opposite end of the third linkage 38 connects the second platform , wherein a third angle 26 is existed between the second linkage 36 and the third linkage 38 . due to one end of the second linkage 36 is connected to the first base 48 by a ball bearing and a bolt so as to function as a fixed axle , the second linkage 36 can only move left and right . when the first ballscrew 32 is driven by the first motor 46 to rotate , the first linkage 34 , the second linkage 36 and the third linkage 38 are driven simultaneously by the first ballscrew 32 and cause the second angle 24 and the third angle 26 changing along with their movement . since the second linkage 36 is fixed on the first base 48 , the third linkage is non - movable . moreover , in order to connect three linkages with the second base 14 and the first ballscrew 32 on a same horizontal plane , the three linkages have a supporting frame 50 which supports the three linkages having the same height as the second base 14 and the first ballscrew 32 . in that way , the suspended three linkages can apply force properly . additionally , the second linkage 36 is connected to the first linkage 34 and the third linkage 38 . when the first ballscrew 32 is driven by the first motor 46 to rotate , the three linkages are driven simultaneously by the rotation of the first ballscrew 32 . the second angle 24 and the third angle 26 would change due to the movements of the three linkages , such that the second platform 14 is driven to move along the first predetermined path 54 . in the present invention , the first angle is existed between the extended directions of the second platform 14 and the first ballscrew 32 , wherein the first angle is about 90 °. the second angle is existed between the first linkage 34 and the third linkage 38 , wherein the second angle is between about 0 ° to 90 °. further , the third angle is existed between the second linkage 36 and the third linkage 38 , wherein the third angle is between about 0 ° to 90 °. the first ballscrew 32 , the first linkage 34 , the second linkage 36 , the third linkage 38 , the second platform 14 and the first base 48 are connected by the ball bearing and the bolt in order to decrease frictions therebetween and to decrease the load of the first motor 46 . the present invention further provides a three - link toggle type machine tool , as shown in fig6 , which comprises a first three - link toggle type positioning platform 10 and a second three - link toggle type positioning platform 20 , wherein the first three - link toggle type positioning platform 10 and the second three - link toggle type positioning platform 20 are stacked to form the three - link toggle type machine tool . in addition , a first predetermined path 54 of the first three - link toggle type positioning platform 10 is perpendicular to a second predetermined path 94 of the second three - link toggle type positioning platform 20 . please refer to fig5 since the detail structure of the first three - link toggle type positioning platform 10 does not show in fig6 . the first three - link toggle type positioning platform 10 comprises a first platform 12 , a first motor 46 , a first ballscrew 32 , a second platform 14 , a first linkage 34 , a second linkage 36 and a third linkage 38 . the first motor 46 is disposed on the first platform 12 . the first ballscrew 32 is disposed on the first platform 12 and coupled to the first motor 46 , wherein the first motor 46 is suitable for driving the first ballscrew 32 to rotate . the second platform 14 is disposed on the first platform 12 , wherein the second platform 14 is suitable for moving back and fourth alternately along a first predetermined path 54 , wherein a first angle 22 is existed between an extended direction of the first predetermined path 54 and the first ballscrew 32 . the second linkage 36 is fixed on a first base 48 and is parallel to the first ballscrew 32 and the second platform 14 . the first linkage 34 is disposed between the first ballscrew 32 and the second linkage 36 , wherein a second angle 24 is existed between the first ballscrew 32 and the first linkage 34 . the third linkage 38 is disposed between the second linkage 36 and the second platform 14 , wherein a third angle 26 is existed between the second linkage 36 and the third linkage 38 . moreover , the first linkage 34 , the second linkage 36 and the third linkage 38 are driven simultaneously by the rotation of the first ballscrew 32 , such that the second platform 14 is driven to move along the first predetermined path 54 . referring to fig6 , the second three - link toggle type positioning platform 20 is disposed on the first three - link toggle type positioning platform 10 , wherein the second three - link toggle type positioning platform 20 comprises a second motor 90 , a second ballscrew 78 , a third platform 70 , a fourth linkage 80 , a fifth linkage 82 , and a sixth linkage 84 . the second motor 90 is disposed on the second platform 14 . the second ballscrew 78 is disposed on the second platform 14 and coupled to a second motor 90 , wherein the second motor 90 is suitable for driving the second ballscrew 78 to rotate . the third platform 70 is disposed on the second platform 14 , wherein the third platform 70 is suitable for moving back and fourth alternately along a second predetermined path 94 , wherein a fourth angle 72 is existed between an extended direction of the second predetermined path 94 and the second ballscrew 78 . the fourth linkage 80 is disposed between the second ballscrew 78 and the fifth linkage 82 , wherein a fifth angle 74 is existed between the second ballscrew 78 and the fourth linkage 80 . the fifth linkage 82 is fixed on a second base 92 and is parallel to the second ballscrew 78 and the third platform 70 . the sixth linkage 84 is disposed between the fifth linkage 82 and the third platform 70 , wherein a sixth angle 76 is existed between the fifthlinkage 82 and the sixth linkage 84 . moreover , the fourth linkage 80 , the fifth linkage 82 and the sixth linkage 84 are driven simultaneously by the rotation of the second ballscrew 78 , such that the third platform 70 is driven to move along the second predetermined path 94 . the aforesaid third platform 70 can move back and fourth along the second predetermined path 94 with the help of a second linear bearing 88 and a second slide rail 86 . the present invention comprises a second linear bearing 88 penetrates a second slide rail 86 , wherein two opposite ends of the second slide rail 86 are fixed on repective supporting frames 50 . the length of the second slide rail 86 is equal to that of the second predetermined path 94 . the moving direction of the second linear bearing 88 and the second slide rail 86 is perpendicular to the second ballscrew 78 and the first predetermined path 54 . furthermore , the second linear bearing 88 and the second slide rail 86 are disposed between the second platform 14 and the third platform 70 and fixed on the bilateral sides of the third platform 70 . due to the second linear bearing 88 is a long - shaped cylindrical tube , which is made of iron or other materials , the third platform 70 can not being fixed on it . in the present embodiment , the second linear bearing 88 is fixed in a stable long - shaped quadrate tube in order to form a flat surface , which is disposed between the second platform 14 and the third platform 70 to avoid rotation . the second platform 14 may have a guide groove and the third platform 70 is suitable for moving along the guide groove . the guide groove has a cross - section of v - shape , u - shape , or other shapes . besides , the present embodiment further comprises a ball bearing . the ball bearing is disposed on the second platform 14 and is between the second platform 14 and the third platform 70 , and therefore the third platform 70 may move along the second predetermined path 94 . in brief , the ball bearing may move along the guide groove ( not shown ). the connecting structure for three - link linkage is to connect two opposite ends of the fourth linkage 80 with the second ballscrew 78 and the fifth linkage 82 , wherein a fifth angle 74 is existed between the second ballscrew 78 and the fourth linkage 80 . one opposite end of the fifth linkage 82 is fixed on the second base 92 , wherein the second base 92 can support the fifth linkage 82 . one end of the sixth linkage 84 connects to the fifth linkage 52 where near the second base 92 . moreover , one opposite end of the sixth linkage 84 connects the third platform 70 , wherein a sixth angle 76 is existed between the fifth linkage 82 and the sixth linkage 84 . due to one end of the fifth linkage 82 is connected to the second base 92 by a ball bearing and a bolt 52 so as to function as a fixed axle , the fifth linkage 82 can only move left and right . when the second ballscrew 78 is driven by the second motor 90 to rotate , the fourth linkage 80 , the fifth linkage 82 and the sixth linkage 84 are driven simultaneously by the second ballscrew 78 and cause the fifth angle 74 and the sixth angle 76 changing along with their movement . since the fifth linkage 82 is fixed on the second base 92 , the third linkage is non - movable . moreover , in order to connect three linkages with the third base 70 and the second ballscrew 78 on a same horizontal plane , the three linkages have a supporting frame 50 which supports the three linkages having the same height as the third base 70 and the second ballscrew 78 . in that way , the suspended three linkages can apply force properly . additionally , the fifth linkage 82 is connected to the fourth linkage 80 and the sixth linkage 84 . when the second ballscrew 78 is driven by the second motor 90 to rotate , the three linkages are driven simultaneously by the rotation of the second ballscrew 78 . the fifth angle 74 and the sixth angle 76 would change due to the movements of the three linkages , such that the third platform 70 is driven to move along the second predetermined path 94 . in the present invention , the fourth angle is existed between the extended directions of the third platform 70 and the second ballscrew 78 , wherein the fourth angle is about 90 °. the fifth angle is existed between the fourth linkage 80 and the fifth linkage 82 , wherein the fifth angle is between about 0 ° to 90 °. further , the sixth angle is existed between the fifth linkage 82 and the sixth linkage 84 , wherein the sixth angle is between about 0 ° to 90 °. the second ballscrew 78 , the fourth linkage 80 , the fifth linkage 82 , the sixth linkage 84 , the third platform 70 and the second base 92 are connected by the ball bearing and the bolt 52 in order to decrease frictions therebetween and to decrease the load of the second motor 90 . then , a laser meter is being used to measure the amount of movement of the second platform 14 of the first three - link toggle type positioning platform 10 . placing a beam splitter in front of the laser meter and a reflecting mirror on the second platform and then aligned for reflecting laser beam . a measuring method is as follows . the beam splitter is used for splitting the laser beam into a reference beam and a beam to be measured when it enters . the beam to be measured is then reflected back on the same path by the reflecting minor and meets the reference beam . after analyzed by a computer , the displacement of the second platform can be known . fig7 is numerical analysis data of the first three - link toggle type positioning platform according to one embodiment of the present invention , wherein the data is calculated by the measuring method described in the above paragraph . the relationship between number of turns of motor and amount of movement of platform can be calculated according to the data shown in fig7 and being compared with theoretical value in fig8 . the maximum number of turns of motor in the present invention is only 50 turns less than that of the theory which has 100 turns . however , according to the data collected from 5 to 50 turns of the motor , the amount of movement of the second platform in one embodiment is very similar to theoretical value , that is , when the number of turns of motor in one embodiment of the present invention reaches 100 turns , the resulting value will be similar to theoretical value , too . although the materials used in the present embodiment may have large effect to the experimental data , it is not under discussion here . the present invention provides a positioning platform with a toggle - type mechanism to improve its positioning precision . moreover , the present invention provides a positioning platform with a three - link toggle type mechanism which makes it move faster than a single - link toggle type mechanism the above - described embodiment of the present invention is intended to be illustrative only . numerous alternative embodiments may be devised by persons skilled in the art without departing from the scope of the following claims .