**Full Lists**
I have OCD so I took the liberty to reorganize Jonathan's lists with the corrections he provided, mainly for visual ease. Thanks to Jonathan for his contribution to this thread.

Here are some numbers that should illustrate the trends that I have been talking about.

First triplet of number lists involves a Thales circle diameter of 345mm, and a swingarm length of 115mm (one-third the Thales circle diameter). The variable is in where the three null points have been set. As you will see, shifting the null points alters how the tracking error is distributed across the LP, and the maximum tracking error, but it also affects the optimal guidearm length (and the location of pivot position P, but let's leave that for another time).

If you refer to the drawing that directdriver posted, the B-C-C "triangle" has been chopped up into 0.25-degree segments for analysis. A finer grid than 0.25 degrees will give more accurate results, but would involve more work. For the time being, I chose to use a moderate grid that is fine enough to establish the general trends, but isn't too taxing of a workload.

In each list, the lines marked with # are the null points that I chose. The lines marked with * are the tracking error peaks that resulted, with the caveat that a finer grid than 0.25 degrees may show slightly different results. Line 64 is the innermost LP groove, line 01 is the outermost LP groove, but the 0.25-degree grid starts with line 64, making the difference between lines 01 and 02 less than 0.25 degrees (considerably less, in this particular case).

After the line number (01-64), the first number in each line is the distance between the measurement point and the platter spindle (strictly speaking, this isn't the LP radius, since it includes the distances by which the momentary stylus position C oversteps or understeps the circumference of the Thales circle).

The second number in each line is the angle between the BC (line between pivot and stylus) and CA (line between stylus and platter spindle).

Any difference between the second number in each line and 90 degrees is the tracking error, which is the third number in each line. I have only added the third number for the tracking error peaks - so that they stand out on their own.

Once again these employ a Thales circle diameter of 345mm, but list 4 reduces the swingarm length to 100mm (15mm less than the 115mm used in lists 1, 2 & 3), while list 5 increases the swingarm length to 130mm (15mm more than the 115mm used in lists 1, 2 & 3). The tracking error peaks could presumably be reduced a little by adjusting the null points, but only to the extent of better "averaging out" the errors.

Altering the swingarm length (while keeping a fixed Thales circle diameter) not only changes the tracking errors, it also changes the optimal guidearm length (although this may not be obvious from just looking at the number lists, it will be obvious when you try to work out the optimal geometry).

The second number in each line is the angle between the BC (line between pivot and stylus) and CA (line between stylus and platter spindle).

jonathan carr

------------------------------------

List 1: Thales circle diameter 345mm, swingarm length 115mm, guidearm length 97.45159mm

01. 146.60000mm 90.01405 degrees +0.01405 (*)

02. 146.31647mm 90.01324 degrees

03. 144.95182mm 90.00949 degrees

04. 143.58441mm 90.00605 degrees

05. 142.21426mm 90.00288 degrees

06. 140.84141mm 90.00000 degrees (#)

07. 139.46588mm 89.99738 degrees

08. 138.08770mm 89.99502 degrees

09. 136.70688mm 89.99291 degrees

10. 135.32346mm 89.99103 degrees

11. 133.93747mm 89.98939 degrees

12. 132.54892mm 89.98797 degrees

13. 131.15786mm 89.98676 degrees

14. 129.76429mm 89.98575 degrees

15. 128.36826mm 89.98494 degrees

16. 126.96978mm 89.98432 degrees

17. 125.56888mm 89.98388 degrees

18. 124.16559mm 89.98360 degrees

19. 122.75994mm 89.98349 degrees -0.01651 (*)

20. 121.35195mm 89.98354 degrees

21. 119.94165mm 89.98373 degrees

22. 118.52907mm 89.98406 degrees

23. 117.11423mm 89.98452 degrees

24. 115.69716mm 89.98511 degrees

25. 114.27788mm 89.98581 degrees

26. 112.85644mm 89.98661 degrees

27. 111.43284mm 89.98751 degrees

28. 110.00712mm 89.98850 degrees

29. 108.57931mm 89.98957 degrees

30. 107.14943mm 89.99072 degrees

31. 105.71751mm 89.99193 degrees

32. 104.28358mm 89.99319 degrees

33. 102.84766mm 89.99450 degrees

34. 101.40978mm 89.99584 degrees

35. 99.969980mm 89.99721 degrees

36. 98.528270mm 89.99860 degrees

37. 97.084680mm 90.00000 degrees (#)

38. 95.639250mm 90.00139 degrees

39. 94.191990mm 90.00277 degrees

40. 92.742950mm 90.00413 degrees

41. 91.292130mm 90.00545 degrees

42. 89.839580mm 90.00672 degrees

43. 88.385320mm 90.00792 degrees

44. 86.929380mm 90.00906 degrees

45. 85.471780mm 90.01011 degrees

46. 84.012550mm 90.01105 degrees

47. 82.551720mm 90.01188 degrees

48. 81.089320mm 90.01258 degrees

49. 79.625380mm 90.01312 degrees

50. 78.159930mm 90.01350 degrees

51. 76.692980mm 90.01369 degrees +0.01369 (*)

52. 75.224570mm 90.01367 degrees

53. 73.754730mm 90.01342 degrees

54. 72.283490mm 90.01292 degrees

55. 70.810870mm 90.01215 degrees

56. 69.336910mm 90.01107 degrees

57. 67.861620mm 90.00965 degrees

58. 66.385040mm 90.00787 degrees

59. 64.907200mm 90.00570 degrees

60. 63.428120mm 90.00309 degrees

61. 61.947830mm 90.00000 degrees (#)

62. 60.466370mm 89.99639 degrees

63. 58.983750mm 89.99222 degrees

64. 57.500000mm 89.98743 degrees -0.01257 (*)

---------------------------------------

List 2: Thales circle diameter 345mm, swingarm length 115mm, guidearm length 97.55125mm

01. 146.60000mm 90.01332 degrees +0.01332

02. 146.31647mm 90.01254 degrees

03. 144.95182mm 90.00898 degrees

04. 143.58441mm 90.00571 degrees

05. 142.21426mm 90.00272 degrees

06. 140.84141mm 90.00000 degrees (#)

07. 139.46588mm 89.99754 degrees

08. 138.08770mm 89.99534 degrees

09. 136.70688mm 89.99338 degrees

10. 135.32346mm 89.99166 degrees

11. 133.93747mm 89.99016 degrees

12. 132.54892mm 89.98887 degrees

13. 131.15786mm 89.98780 degrees

14. 129.76429mm 89.98692 degrees

15. 128.36825mm 89.98624 degrees

16. 126.96977mm 89.98574 degrees

17. 125.56888mm 89.98541 degrees

18. 124.16559mm 89.98525 degrees -0.01475 (*)

19. 122.75994mm 89.98525 degrees -0.01475 (*)

20. 121.35195mm 89.98540 degrees

21. 119.94165mm 89.98569 degrees

22. 118.52907mm 89.98611 degrees

23. 117.11423mm 89.98666 degrees

24. 115.69716mm 89.98733 degrees

25. 114.27788mm 89.98811 degrees

26. 112.85644mm 89.98899 degrees

27. 111.43284mm 89.98995 degrees

28. 110.00712mm 89.99101 degrees

29. 108.57931mm 89.99214 degrees

30. 107.14943mm 89.99333 degrees

31. 105.71751mm 89.99459 degrees

32. 104.28358mm 89.99589 degrees

33. 102.84766mm 89.99723 degrees

34. 101.40978mm 89.99861 degrees

35. 99.969980mm 90.00000 degrees (#)

36. 98.528270mm 90.00140 degrees

37. 97.084680mm 90.00281 degrees

38. 95.639250mm 90.00420 degrees

39. 94.191990mm 90.00558 degrees

40. 92.742950mm 90.00692 degrees

41. 91.292130mm 90.00822 degrees

42. 89.839580mm 90.00946 degrees

43. 88.385320mm 90.01063 degrees

44. 86.929380mm 90.01172 degrees

45. 85.471780mm 90.01271 degrees

46. 84.012550mm 90.01359 degrees

47. 82.551720mm 90.01434 degrees

48. 81.089330mm 90.01495 degrees

49. 79.625380mm 90.01540 degrees

50. 78.159930mm 90.01567 degrees

51. 76.692980mm 90.01574 degrees +0.01574 (*)

52. 75.224570mm 90.01559 degrees

53. 73.754740mm 90.01519 degrees

54. 72.283490mm 90.01453 degrees

55. 70.810870mm 90.01358 degrees

56. 69.336910mm 90.01231 degrees

57. 67.861620mm 90.01068 degrees

58. 66.385040mm 90.00868 degrees

59. 64.907200mm 90.00625 degrees

60. 63.428120mm 90.00338 degrees

61. 61.947830mm 90.00000 degrees (#)

62. 60.466370mm 89.99608 degrees

63. 58.983750mm 89.99157 degrees

64. 57.500000mm 89.98641 degrees -0.01359

-------------------------------------

List 3: Thales circle diameter 345mm, swingarm length 115mm, guidearm length 97.50125mm

01. 146.60000mm 90.01369 degrees +0.01369

02. 146.31647mm 90.01289 degrees

03. 144.95182mm 90.00924 degrees

04. 143.58441mm 90.00588 degrees

05. 142.21426mm 90.00280 degrees

06. 140.84141mm 90.00000 degrees (#)

07. 139.46588mm 89.99746 degrees

08. 138.08770mm 89.99518 degrees

09. 136.70688mm 89.99314 degrees

10. 135.32346mm 89.99134 degrees

11. 133.93747mm 89.98977 degrees

12. 132.54892mm 89.98842 degrees

13. 131.15786mm 89.98728 degrees

14. 129.76429mm 89.98634 degrees

15. 128.36825mm 89.98599 degrees

16. 126.96977mm 89.98503 degrees

17. 125.56888mm 89.98464 degrees

18. 124.16559mm 89.98443 degrees

19. 122.75994mm 89.98437 degrees -0.01563 (*)

20. 121.35195mm 89.98447 degrees

21. 119.94165mm 89.98471 degrees

22. 118.52907mm 89.98509 degrees

23. 117.11423mm 89.98559 degrees

24. 115.69716mm 89.98622 degrees

25. 114.27788mm 89.98695 degrees

26. 112.85644mm 89.98779 degrees

27. 111.43284mm 89.98873 degrees

28. 110.00712mm 89.98975 degrees

29. 108.57931mm 89.98085 degrees

30. 107.14943mm 89.99202 degrees

31. 105.71751mm 89.99325 degrees

32. 104.28358mm 89.99454 degrees

33. 102.84766mm 89.99586 degrees

34. 101.40978mm 89.99722 degrees

35. 99.969980mm 89.99860 degrees

36. 98.528270mm 90.00000 degrees (#)

37. 97.084680mm 90.00140 degrees

38. 95.639250mm 90.00279 degrees

39. 94.191990mm 90.00417 degrees

40. 92.742950mm 90.00552 degrees

41. 91.292130mm 90.00683 degrees

42. 89.839580mm 90.00808 degrees

43. 88.385320mm 90.00927 degrees

44. 86.929380mm 90.01038 degrees

45. 85.471780mm 90.01140 degrees

46. 84.012550mm 90.01232 degrees

47. 82.551720mm 90.01311 degrees

48. 81.089330mm 90.01376 degrees

49. 79.625380mm 90.01426 degrees

50. 78.159930mm 90.01458 degrees

51. 76.692980mm 90.01471 degrees +0.01471 (*)

52. 75.224570mm 90.01462 degrees

53. 73.754740mm 90.01430 degrees

54. 72.283490mm 90.01373 degrees

55. 70.810870mm 90.01286 degrees

56. 69.336910mm 90.01168 degrees

57. 67.861620mm 90.01017 degrees

58. 66.385040mm 90.00827 degrees

59. 64.907200mm 90.00598 degrees

60. 63.428120mm 90.00323 degrees

61. 61.947830mm 90.00000 degrees (#)

62. 60.466370mm 89.99624 degrees

63. 58.983750mm 89.99190 degrees

64. 57.500000mm 89.98692 degrees -0.01308

--------------------------------------------

List 4: Thales circle diameter 345mm, swingarm length 100mm, guidearm length 106.29313mm

01. 146.60000mm 90.01039 degrees +0.01039

02. 146.31647mm 90.00978 degrees

03. 144.95182mm 90.00702 degrees

04. 143.58441mm 90.00447 degrees

05. 142.21426mm 90.00213 degrees

06. 140.84141mm 90.00000 degrees (#)

07. 139.46588mm 89.99807 degrees

08. 138.08770mm 89.99633 degrees

09. 136.70688mm 89.99477 degrees

10. 135.32346mm 89.99340 degrees

11. 133.93747mm 89.99219 degrees

12. 132.54892mm 89.99115 degrees

13. 131.15785mm 89.99028 degrees

14. 129.76429mm 89.98955 degrees

15. 128.36825mm 89.98898 degrees

16. 126.96977mm 89.98854 degrees

17. 125.56888mm 89.98824 degrees

18. 124.16559mm 89.98807 degrees

19. 122.75994mm 89.98802 degrees -0.01198 (*)

20. 121.35195mm 89.98809 degrees

21. 119.94165mm 89.98827 degrees

22. 118.52906mm 89.98855 degrees

23. 117.11422mm 89.98894 degrees

24. 115.69716mm 89.98941 degrees

25. 114.27788mm 89.98997 degrees

26. 112.85643mm 89.99062 degrees

27. 111.43284mm 89.99133 degrees

28. 110.00712mm 89.99211 degrees

29. 108.57931mm 89.99296 degrees

30. 107.14943mm 89.99386 degrees

31. 105.71751mm 89.99480 degrees

32. 104.28358mm 89.99579 degrees

33. 102.84766mm 89.99681 degrees

34. 101.40978mm 89.99786 degrees

35. 99.969980mm 89.99892 degrees

36. 98.528270mm 90.00000 degrees (#)

37. 97.084680mm 90.00108 degrees

38. 95.639250mm 90.00216 degrees

39. 94.191990mm 90.00322 degrees

40. 92.742950mm 90.00427 degrees

41. 91.292130mm 90.00528 degrees

42. 89.839580mm 90.00625 degrees

43. 88.385320mm 90.00717 degrees

44. 86.929380mm 90.00803 degrees

45. 85.471780mm 90.00883 degrees

46. 84.012550mm 90.00954 degrees

47. 82.551720mm 90.01015 degrees

48. 81.089320mm 90.01066 degrees

49. 79.625380mm 90.01105 degrees

50. 78.159920mm 90.01130 degrees

51. 76.692980mm 90.01140 degrees +0.01140 (*)

52. 75.224570mm 90.01134 degrees

53. 73.754730mm 90.01110 degrees

54. 72.283490mm 90.01065 degrees

55. 70.810870mm 90.00998 degrees

56. 69.336910mm 90.00907 degrees

57. 67.861620mm 90.000789degrees

58. 66.385040mm 90.00643 degrees

59. 64.907200mm 90.00464 degrees

60. 63.428120mm 90.00251 degrees

61. 61.947830mm 90.00000 degrees (#)

62. 60.466370mm 89.99708 degrees

63. 58.983750mm 89.99370 degrees

64. 57.500000mm 89.98983 degrees -0.01017

---------------------------------------------

List 5: Thales circle diameter 345mm, swingarm length 130mm, guidearm length 89.08119mm

01. 146.60001mm 90.01789 degrees +0.01789

02. 146.31647mm 90.01685 degrees

03. 144.95182mm 90.01206 degrees

04. 143.58441mm 90.00767 degrees

05. 142.21426mm 90.00365 degrees

06. 140.84141mm 90.00000 degrees (#)

07. 139.46588mm 89.99670 degrees

08. 138.0877mm 89.99373 degrees

09. 136.70688mm 89.99108 degrees

10. 135.32346mm 89.98875 degrees

11. 133.93747mm 89.98672 degrees

12. 132.54893mm 89.98497 degrees

13. 131.15786mm 89.98350 degrees

14. 129.76429mm 89.98229 degrees

15. 128.36826mm 89.98134 degrees

16. 126.96978mm 89.98062 degrees

17. 125.56888mm 89.98013 degrees

18. 124.16559mm 89.97987 degrees

19. 122.75994mm 89.97981 degrees -0.02019 (*)

20. 121.35195mm 89.97994 degrees

21. 119.94165mm 89.98027 degrees

22. 118.52907mm 89.98076 degrees

23. 117.11423mm 89.98143 degrees

24. 115.69716mm 89.98224 degrees

25. 114.27789mm 89.98320 degrees

26. 112.85644mm 89.98429 degrees

27. 111.43284mm 89.98550 degrees

28. 110.00712mm 89.98682 degrees

29. 108.57931mm 89.98824 degrees

30. 107.14943mm 89.98975 degrees

31. 105.71751mm 89.99134 degrees

32. 104.28358mm 89.99299 degrees

33. 102.84766mm 89.99469 degrees

34. 101.40978mm 89.99643 degrees

35. 99.969980mm 89.99821 degrees

36. 98.528270mm 90.00000 degrees (#)

37. 97.084680mm 90.00179 degrees

38. 95.639250mm 90.00358 degrees

39. 94.191990mm 90.00534 degrees

40. 92.742950mm 90.00706 degrees

41. 91.292130mm 90.00873 degrees

42. 89.839580mm 90.01033 degrees

43. 88.385320mm 90.01185 degrees

44. 86.929380mm 90.01326 degrees

45. 85.471780mm 90.01456 degrees

46. 84.012550mm 90.01572 degrees

47. 82.551720mm 90.01673 degrees

48. 81.089330mm 90.01755 degrees

49. 79.625380mm 90.01818 degrees

50. 78.159930mm 90.01859 degrees

51. 76.692980mm 90.01875 degrees +0.01875 (*)

52. 75.224570mm 90.01863 degrees

53. 73.754740mm 90.01822 degrees

54. 72.283490mm 90.01748 degrees

55. 70.810870mm 90.01637 degrees

56. 69.336910mm 90.01487 degrees

57. 67.861620mm 90.01293 degrees

58. 66.385040mm 90.01052 degrees

59. 64.907200mm 90.00760 degrees

60. 63.428120mm 90.00411 degrees

61. 61.947830mm 90.00000 degrees (#)

62. 60.466370mm 89.99522 degrees

63. 58.983750mm 89.98970 degrees

64. 57.500000mm 89.98339 degrees -0.01661

--------------------------------------------