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content/article/chen00_ident_decoup_contr_flexur_joint_hexap.md
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@@ -8,9 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference
: <sup id="ba05ff213f8e5963d91559d95becfbdb"><a class="reference-link" href="#chen00_ident_decoup_contr_flexur_joint_hexap" title="Yixin Chen \&amp; McInroy, Identification and Decoupling Control of Flexure Jointed Hexapods, nil, in in: {Proceedings 2000 ICRA. Millennium Conference. IEEE
International Conference on Robotics and Automation. Symposia
Proceedings (Cat. No.00CH37065)}, edited by (2000)">(Yixin Chen \& McInroy, 2000)</a></sup>
: ([Chen and McInroy 2000](#orgd504c56))
Author(s)
: Chen, Y., & McInroy, J.
@@ -45,10 +43,9 @@ The algorithm derived herein removes these constraints, thus greatly expanding t
## Dynamic Model of Flexure Jointed Hexapods {#dynamic-model-of-flexure-jointed-hexapods}
The derivation of the dynamic model is done in <sup id="5da427f78c552aa92cd64c2a6df961f1"><a class="reference-link" href="#mcinroy99_dynam" title="McInroy, Dynamic modeling of flexure jointed hexapods for control purposes, nil, in in: {Proceedings of the 1999 IEEE International Conference on
Control Applications (Cat. No.99CH36328)}, edited by (1999)">(McInroy, 1999)</a></sup> ([Notes]({{< relref "mcinroy99_dynam" >}})).
The derivation of the dynamic model is done in ([McInroy 1999](#orgbf9df90)) ([Notes]({{< relref "mcinroy99_dynam" >}})).
<a id="org81e0a96"></a>
<a id="org56416c1"></a>
{{< figure src="/ox-hugo/chen00_flexure_hexapod.png" caption="Figure 1: A flexured joint Hexapod. {P} is a cartesian coordiante frame located at (and rigidly connected to) the payload's center of mass. {B} is a frame attached to the (possibly moving) base, and {U} is a universal inertial frame of reference" >}}
@@ -102,7 +99,9 @@ where
## Experimental Results {#experimental-results}
# Bibliography
<a class="bibtex-entry" id="chen00_ident_decoup_contr_flexur_joint_hexap">Chen, Y., & McInroy, J., *Identification and decoupling control of flexure jointed hexapods*, In , Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065) (pp. ) (2000). : .</a> [↩](#ba05ff213f8e5963d91559d95becfbdb)
<a class="bibtex-entry" id="mcinroy99_dynam">McInroy, J., *Dynamic modeling of flexure jointed hexapods for control purposes*, In , Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328) (pp. ) (1999). : .</a> [↩](#5da427f78c552aa92cd64c2a6df961f1)
## Bibliography {#bibliography}
<a id="orgd504c56"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.
<a id="orgbf9df90"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.

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content/article/dasgupta00_stewar_platf_manip.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference
: <sup id="ad17e03f0fbbcc1a070557d7b5a0e1e1"><a class="reference-link" href="#dasgupta00_stewar_platf_manip" title="Bhaskar Dasgupta \&amp; Mruthyunjaya, The Stewart Platform Manipulator: a Review, {Mechanism and Machine Theory}, v(1), 15-40 (2000).">(Bhaskar Dasgupta \& Mruthyunjaya, 2000)</a></sup>
: ([Dasgupta and Mruthyunjaya 2000](#orge03a23b))
Author(s)
: Dasgupta, B., & Mruthyunjaya, T.
@@ -33,5 +33,7 @@ Year
The generalized Stewart platforms consists of two rigid bodies (referred to as the base and the platoform) connected through six extensible legs, each with sherical joints at both ends.
# Bibliography
<a class="bibtex-entry" id="dasgupta00_stewar_platf_manip">Dasgupta, B., & Mruthyunjaya, T., *The stewart platform manipulator: a review*, Mechanism and Machine Theory, *35(1)*, 15–40 (2000). http://dx.doi.org/10.1016/s0094-114x(99)00006-3</a> [↩](#ad17e03f0fbbcc1a070557d7b5a0e1e1)
## Bibliography {#bibliography}
<a id="orge03a23b"></a>Dasgupta, Bhaskar, and T.S. Mruthyunjaya. 2000. “The Stewart Platform Manipulator: A Review.” _Mechanism and Machine Theory_ 35 (1):15–40. <https://doi.org/10.1016/s0094-114x(99)>00006-3.

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content/article/fleming13_review_nanom_resol_posit_sensor.md
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@@ -8,7 +8,7 @@ Tags
: [Position Sensors]({{< relref "position_sensors" >}})
Reference
: <sup id="3fb5b61524290e36d639a4fac65703d0"><a class="reference-link" href="#fleming13_review_nanom_resol_posit_sensor" title="Andrew Fleming, A Review of Nanometer Resolution Position Sensors: Operation and Performance, {Sensors and Actuators A: Physical}, v(nil), 106-126 (2013).">(Andrew Fleming, 2013)</a></sup>
: ([Fleming 2013](#org66efc4b))
Author(s)
: Fleming, A. J.
@@ -33,7 +33,7 @@ Usually quoted as a percentage of the fill-scale range (FSR):
With \\(e\_m(v)\\) is the mapping error.
<a id="org6e00657"></a>
<a id="org51fba0c"></a>
{{< figure src="/ox-hugo/fleming13_mapping_error.png" caption="Figure 1: The actual position versus the output voltage of a position sensor. The calibration function \\(f\_{cal}(v)\\) is an approximation of the sensor mapping function \\(f\_a(v)\\) where \\(v\\) is the voltage resulting from a displacement \\(x\\). \\(e\_m(v)\\) is the residual error." >}}
@@ -42,7 +42,7 @@ With \\(e\_m(v)\\) is the mapping error.
If the shape of the mapping function actually varies with time, the maximum error due to drift must be evaluated by finding the worst-case mapping error.
<a id="org076fb4b"></a>
<a id="org2b35a7e"></a>
{{< figure src="/ox-hugo/fleming13_drift_stability.png" caption="Figure 2: The worst case range of a linear mapping function \\(f\_a(v)\\) for a given error in sensitivity and offset." >}}
@@ -147,9 +147,9 @@ The empirical rule states that there is a \\(99.7\%\\) probability that a sample
This if we define the resolution as \\(\delta = 6 \sigma\\), we will referred to as the \\(6\sigma\text{-resolution}\\).
Another important parameter that must be specified when quoting resolution is the sensor bandwidth.
There is usually a trade-off between bandwidth and resolution (figure [3](#org92eeb72)).
There is usually a trade-off between bandwidth and resolution (figure [3](#org40574f2)).
<a id="org92eeb72"></a>
<a id="org40574f2"></a>
{{< figure src="/ox-hugo/fleming13_tradeoff_res_bandwidth.png" caption="Figure 3: The resolution versus banwidth of a position sensor." >}}
@@ -181,8 +181,10 @@ A convenient method for reporting this ratio is in parts-per-million (ppm):
| Interferometer | Meters | | 0.5 nm | >100kHz | 1 ppm FSR |
| Encoder | Meters | | 6 nm | >100kHz | 5 ppm FSR |
# Bibliography
<a class="bibtex-entry" id="fleming13_review_nanom_resol_posit_sensor">Fleming, A. J., *A review of nanometer resolution position sensors: operation and performance*, Sensors and Actuators A: Physical, *190(nil)*, 106–126 (2013). http://dx.doi.org/10.1016/j.sna.2012.10.016</a> [↩](#3fb5b61524290e36d639a4fac65703d0)
## Bibliography {#bibliography}
<a id="org66efc4b"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>.
## Backlinks {#backlinks}

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content/article/furqan17_studies_stewar_platf_manip.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference
: <sup id="cc10fe9545c7c381cc2b610e8f91a071"><a class="reference-link" href="#furqan17_studies_stewar_platf_manip" title="Mohd Furqan, Mohd Suhaib \&amp; Nazeer Ahmad, Studies on Stewart Platform Manipulator: a Review, {Journal of Mechanical Science and Technology}, v(9), 4459-4470 (2017).">(Mohd Furqan {\it et al.}, 2017)</a></sup>
: ([Furqan, Suhaib, and Ahmad 2017](#org5774b90))
Author(s)
: Furqan, M., Suhaib, M., & Ahmad, N.
@@ -18,5 +18,7 @@ Year
Lots of references.
# Bibliography
<a class="bibtex-entry" id="furqan17_studies_stewar_platf_manip">Furqan, M., Suhaib, M., & Ahmad, N., *Studies on stewart platform manipulator: a review*, Journal of Mechanical Science and Technology, *31(9)*, 4459–4470 (2017). http://dx.doi.org/10.1007/s12206-017-0846-1</a> [↩](#cc10fe9545c7c381cc2b610e8f91a071)
## Bibliography {#bibliography}
<a id="org5774b90"></a>Furqan, Mohd, Mohd Suhaib, and Nazeer Ahmad. 2017. “Studies on Stewart Platform Manipulator: A Review.” _Journal of Mechanical Science and Technology_ 31 (9):4459–70. <https://doi.org/10.1007/s12206-017-0846-1>.

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content/article/furutani04_nanom_cuttin_machin_using_stewar.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference
: <sup id="bedab298599c84f60236313ebaad2714"><a class="reference-link" href="#furutani04_nanom_cuttin_machin_using_stewar" title="Katsushi Furutani, Michio Suzuki \&amp; Ryusei Kudoh, Nanometre-Cutting Machine Using a Stewart-Platform Parallel Mechanism, {Measurement Science and Technology}, v(2), 467-474 (2004).">(Katsushi Furutani {\it et al.}, 2004)</a></sup>
: ([Furutani, Suzuki, and Kudoh 2004](#org934975a))
Author(s)
: Furutani, K., Suzuki, M., & Kudoh, R.
@@ -34,5 +34,7 @@ Possible sources of error:
To minimize the errors, a calibration is done between the required leg length and the wanted platform pose.
Then, it is fitted with 4th order polynomial and included in the control architecture.
# Bibliography
<a class="bibtex-entry" id="furutani04_nanom_cuttin_machin_using_stewar">Furutani, K., Suzuki, M., & Kudoh, R., *Nanometre-cutting machine using a stewart-platform parallel mechanism*, Measurement Science and Technology, *15(2)*, 467–474 (2004). http://dx.doi.org/10.1088/0957-0233/15/2/022</a> [↩](#bedab298599c84f60236313ebaad2714)
## Bibliography {#bibliography}
<a id="org934975a"></a>Furutani, Katsushi, Michio Suzuki, and Ryusei Kudoh. 2004. “Nanometre-Cutting Machine Using a Stewart-Platform Parallel Mechanism.” _Measurement Science and Technology_ 15 (2):467–74. <https://doi.org/10.1088/0957-0233/15/2/022>.

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content/article/gao15_measur_techn_precis_posit.md
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@@ -8,7 +8,7 @@ Tags
: [Position Sensors]({{< relref "position_sensors" >}})
Reference
: <sup id="b820b918ced36901ea0ad4bf653202c6"><a class="reference-link" href="#gao15_measur_techn_precis_posit" title="Gao, Kim, Bosse, Haitjema, , Chen, Lu, Knapp, Weckenmann, , Estler \&amp; Kunzmann, Measurement Technologies for Precision Positioning, {CIRP Annals}, v(2), 773-796 (2015).">(Gao {\it et al.}, 2015)</a></sup>
: ([Gao et al. 2015](#org3775d30))
Author(s)
: Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., …
@@ -16,5 +16,7 @@ Author(s)
Year
: 2015
# Bibliography
<a class="bibtex-entry" id="gao15_measur_techn_precis_posit">Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., …, *Measurement technologies for precision positioning*, CIRP Annals, *64(2)*, 773–796 (2015). http://dx.doi.org/10.1016/j.cirp.2015.05.009</a> [↩](#b820b918ced36901ea0ad4bf653202c6)
## Bibliography {#bibliography}
<a id="org3775d30"></a>Gao, W., S.W. Kim, H. Bosse, H. Haitjema, Y.L. Chen, X.D. Lu, W. Knapp, A. Weckenmann, W.T. Estler, and H. Kunzmann. 2015. “Measurement Technologies for Precision Positioning.” _CIRP Annals_ 64 (2):773–96. <https://doi.org/10.1016/j.cirp.2015.05.009>.

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content/article/garg07_implem_chall_multiv_contr.md
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@@ -8,8 +8,7 @@ Tags
: [Multivariable Control]({{< relref "multivariable_control" >}})
Reference
: <sup id="07f63c751c1d9fcfe628178688f7ec24"><a class="reference-link" href="#garg07_implem_chall_multiv_contr" title="Sanjay Garg, Implementation Challenges for Multivariable Control: What you did not learn in school!, nil, in in: {AIAA Guidance, Navigation and Control Conference and
Exhibit}, edited by (2007)">(Sanjay Garg, 2007)</a></sup>
: ([Garg 2007](#org2f331c4))
Author(s)
: Garg, S.
@@ -35,5 +34,7 @@ The control rate should be weighted appropriately in order to not saturate the s
- importance of scaling the plant prior to synthesis and also replacing pure integrators with slow poles
# Bibliography
<a class="bibtex-entry" id="garg07_implem_chall_multiv_contr">Garg, S., *Implementation challenges for multivariable control: what you did not learn in school!*, In , AIAA Guidance, Navigation and Control Conference and Exhibit (pp. ) (2007). : .</a> [↩](#07f63c751c1d9fcfe628178688f7ec24)
## Bibliography {#bibliography}
<a id="org2f331c4"></a>Garg, Sanjay. 2007. “Implementation Challenges for Multivariable Control: What You Did Not Learn in School!” In _AIAA Guidance, Navigation and Control Conference and Exhibit_, nil. <https://doi.org/10.2514/6.2007-6334>.

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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Active Damping]({{< relref "active_damping" >}})
Reference
: <sup id="10e535e895bdcd6b921bff33ef68cd81"><a class="reference-link" href="#hanieh03_activ_stewar" title="Hanieh, Active isolation and damping of vibrations via Stewart platform (2003).">(Hanieh, 2003)</a></sup>
: ([Hanieh 2003](#org16a7ca0))
Author(s)
: Hanieh, A. A.
@@ -16,5 +16,7 @@ Author(s)
Year
: 2003
# Bibliography
<a class="bibtex-entry" id="hanieh03_activ_stewar">Hanieh, A. A., *Active isolation and damping of vibrations via stewart platform* (2003). Universit{\'e} Libre de Bruxelles, Brussels, Belgium.</a> [↩](#10e535e895bdcd6b921bff33ef68cd81)
## Bibliography {#bibliography}
<a id="org16a7ca0"></a>Hanieh, Ahmed Abu. 2003. “Active Isolation and Damping of Vibrations via Stewart Platform.” Université Libre de Bruxelles, Brussels, Belgium.

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content/article/jiao18_dynam_model_exper_analy_stewar.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference
: <sup id="ee917739f88877d6c2758c1c36565deb"><a class="reference-link" href="#jiao18_dynam_model_exper_analy_stewar" title="Jian Jiao, Ying Wu, Kaiping Yu \&amp; Rui Zhao, Dynamic Modeling and Experimental Analyses of Stewart Platform With Flexible Hinges, {Journal of Vibration and Control}, v(1), 151-171 (2018).">(Jian Jiao {\it et al.}, 2018)</a></sup>
: ([Jiao et al. 2018](#orga81be47))
Author(s)
: Jiao, J., Wu, Y., Yu, K., & Zhao, R.
@@ -16,5 +16,7 @@ Author(s)
Year
: 2018
# Bibliography
<a class="bibtex-entry" id="jiao18_dynam_model_exper_analy_stewar">Jiao, J., Wu, Y., Yu, K., & Zhao, R., *Dynamic modeling and experimental analyses of stewart platform with flexible hinges*, Journal of Vibration and Control, *25(1)*, 151–171 (2018). http://dx.doi.org/10.1177/1077546318772474</a> [↩](#ee917739f88877d6c2758c1c36565deb)
## Bibliography {#bibliography}
<a id="orga81be47"></a>Jiao, Jian, Ying Wu, Kaiping Yu, and Rui Zhao. 2018. “Dynamic Modeling and Experimental Analyses of Stewart Platform with Flexible Hinges.” _Journal of Vibration and Control_ 25 (1):151–71. <https://doi.org/10.1177/1077546318772474>.

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@@ -2,14 +2,13 @@
title = "A new isotropic and decoupled 6-dof parallel manipulator"
author = ["Thomas Dehaeze"]
draft = false
GHissueID = 1
+++
Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference
: <sup id="17295cbc2858c65ecc60d51b450233e3"><a class="reference-link" href="#legnani12_new_isotr_decoup_paral_manip" title="Legnani, Fassi, Giberti, Cinquemani, \&amp; Tosi, A New Isotropic and Decoupled 6-dof Parallel Manipulator, {Mechanism and Machine Theory}, v(nil), 64-81 (2012).">(Legnani {\it et al.}, 2012)</a></sup>
: ([Legnani et al. 2012](#orgfeceab9))
Author(s)
: Legnani, G., Fassi, I., Giberti, H., Cinquemani, S., & Tosi, D.
@@ -23,13 +22,15 @@ Year
Example of generated isotropic manipulator (not decoupled).
<a id="org9b13cfd"></a>
<a id="orgcc7f670"></a>
{{< figure src="/ox-hugo/legnani12_isotropy_gen.png" caption="Figure 1: Location of the leg axes using an isotropy generator" >}}
<a id="org958618e"></a>
<a id="orgb85ffa0"></a>
{{< figure src="/ox-hugo/legnani12_generated_isotropy.png" caption="Figure 2: Isotropic configuration" >}}
# Bibliography
<a class="bibtex-entry" id="legnani12_new_isotr_decoup_paral_manip">Legnani, G., Fassi, I., Giberti, H., Cinquemani, S., & Tosi, D., *A new isotropic and decoupled 6-dof parallel manipulator*, Mechanism and Machine Theory, *58(nil)*, 64–81 (2012). http://dx.doi.org/10.1016/j.mechmachtheory.2012.07.008</a> [↩](#17295cbc2858c65ecc60d51b450233e3)
## Bibliography {#bibliography}
<a id="orgfeceab9"></a>Legnani, G., I. Fassi, H. Giberti, S. Cinquemani, and D. Tosi. 2012. “A New Isotropic and Decoupled 6-Dof Parallel Manipulator.” _Mechanism and Machine Theory_ 58 (nil):64–81. <https://doi.org/10.1016/j.mechmachtheory.2012.07.008>.

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@@ -9,7 +9,7 @@ Tags
Reference
: <sup id="f6d310236552ee92579cf0673a2ca695"><a href="#mcinroy00_desig_contr_flexur_joint_hexap" title="McInroy \&amp; Hamann, Design and Control of Flexure Jointed Hexapods, {IEEE Transactions on Robotics and Automation}, v(4), 372-381 (2000).">(McInroy \& Hamann, 2000)</a></sup>
: ([McInroy and Hamann 2000](#orgc9838dc))
Author(s)
: McInroy, J., & Hamann, J.
@@ -17,5 +17,7 @@ Author(s)
Year
: 2000
# Bibliography
<a id="mcinroy00_desig_contr_flexur_joint_hexap"></a>McInroy, J., & Hamann, J., *Design and control of flexure jointed hexapods*, IEEE Transactions on Robotics and Automation, *16(4)*, 372–381 (2000). http://dx.doi.org/10.1109/70.864229 [↩](#f6d310236552ee92579cf0673a2ca695)
## Bibliography {#bibliography}
<a id="orgc9838dc"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” _IEEE Transactions on Robotics and Automation_ 16 (4):372–81. <https://doi.org/10.1109/70.864229>.

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@@ -8,7 +8,7 @@ Tags
: [Motion Control]({{< relref "motion_control" >}})
Reference
: <sup id="73fd325bd20a6ef8972145e535f38198"><a class="reference-link" href="#oomen18_advan_motion_contr_precis_mechat" title="Tom Oomen, Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems, {IEEJ Journal of Industry Applications}, v(2), 127-140 (2018).">(Tom Oomen, 2018)</a></sup>
: ([Oomen 2018](#orga6f6c0b))
Author(s)
: Oomen, T.
@@ -16,9 +16,11 @@ Author(s)
Year
: 2018
<a id="org5cf2052"></a>
<a id="org2caf38a"></a>
{{< figure src="/ox-hugo/oomen18_next_gen_loop_gain.png" caption="Figure 1: Envisaged developments in motion systems. In traditional motion systems, the control bandwidth takes place in the rigid-body region. In the next generation systemes, flexible dynamics are foreseen to occur within the control bandwidth." >}}
# Bibliography
<a class="bibtex-entry" id="oomen18_advan_motion_contr_precis_mechat">Oomen, T., *Advanced motion control for precision mechatronics: control, identification, and learning of complex systems*, IEEJ Journal of Industry Applications, *7(2)*, 127–140 (2018). http://dx.doi.org/10.1541/ieejjia.7.127</a> [↩](#73fd325bd20a6ef8972145e535f38198)
## Bibliography {#bibliography}
<a id="orga6f6c0b"></a>Oomen, Tom. 2018. “Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems.” _IEEJ Journal of Industry Applications_ 7 (2):127–40. <https://doi.org/10.1541/ieejjia.7.127>.

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@@ -8,7 +8,7 @@ Tags
: [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference
: <sup id="8096d5b2df73551d836ef96b7ca7efa4"><a class="reference-link" href="#preumont07_six_axis_singl_stage_activ" title="Preumont, Horodinca, Romanescu, de, Marneffe, Avraam, Deraemaeker, Bossens, \&amp; Abu Hanieh, A Six-Axis Single-Stage Active Vibration Isolator Based on Stewart Platform, {Journal of Sound and Vibration}, v(3-5), 644-661 (2007).">(Preumont {\it et al.}, 2007)</a></sup>
: ([Preumont et al. 2007](#org89d2c27))
Author(s)
: Preumont, A., Horodinca, M., Romanescu, I., Marneffe, B. d., Avraam, M., Deraemaeker, A., Bossens, F., …
@@ -18,32 +18,34 @@ Year
Summary:
- **Cubic** Stewart platform (Figure [3](#org2d41889))
- **Cubic** Stewart platform (Figure [3](#orgfb89e2d))
- Provides uniform control capability
- Uniform stiffness in all directions
- minimizes the cross-coupling among actuators and sensors of different legs
- Flexible joints (Figure [2](#orgf58a4b4))
- Flexible joints (Figure [2](#org2dfd058))
- Piezoelectric force sensors
- Voice coil actuators
- Decentralized feedback control approach for vibration isolation
- Effect of parasitic stiffness of the flexible joints on the IFF performance (Figure [1](#org6835865))
- Effect of parasitic stiffness of the flexible joints on the IFF performance (Figure [1](#org7e6bce7))
- The Stewart platform has 6 suspension modes at different frequencies.
Thus the gain of the IFF controller cannot be optimal for all the modes.
It is better if all the modes of the platform are near to each other.
- Discusses the design of the legs in order to maximize the natural frequency of the local modes.
- To estimate the isolation performance of the Stewart platform, a scalar indicator is defined as the Frobenius norm of the transmissibility matrix
<a id="org6835865"></a>
<a id="org7e6bce7"></a>
{{< figure src="/ox-hugo/preumont07_iff_effect_stiffness.png" caption="Figure 1: Root locus with IFF with no parasitic stiffness and with parasitic stiffness" >}}
<a id="orgf58a4b4"></a>
<a id="org2dfd058"></a>
{{< figure src="/ox-hugo/preumont07_flexible_joints.png" caption="Figure 2: Flexible joints used for the Stewart platform" >}}
<a id="org2d41889"></a>
<a id="orgfb89e2d"></a>
{{< figure src="/ox-hugo/preumont07_stewart_platform.png" caption="Figure 3: Stewart platform" >}}
# Bibliography
<a class="bibtex-entry" id="preumont07_six_axis_singl_stage_activ">Preumont, A., Horodinca, M., Romanescu, I., Marneffe, B. d., Avraam, M., Deraemaeker, A., Bossens, F., …, *A six-axis single-stage active vibration isolator based on stewart platform*, Journal of Sound and Vibration, *300(3-5)*, 644–661 (2007). http://dx.doi.org/10.1016/j.jsv.2006.07.050</a> [↩](#8096d5b2df73551d836ef96b7ca7efa4)
## Bibliography {#bibliography}
<a id="org89d2c27"></a>Preumont, A., M. Horodinca, I. Romanescu, B. de Marneffe, M. Avraam, A. Deraemaeker, F. Bossens, and A. Abu Hanieh. 2007. “A Six-Axis Single-Stage Active Vibration Isolator Based on Stewart Platform.” _Journal of Sound and Vibration_ 300 (3-5):644–61. <https://doi.org/10.1016/j.jsv.2006.07.050>.

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Reference
: <sup id="e71cc5e3ec879813f2344a6dce1ac11f"><a href="#sayed01_survey_spect_factor_method" title="Sayed \&amp; Kailath, A Survey of Spectral Factorization Methods, {Numerical Linear Algebra with Applications}, v(6-7), 467-496 (2001).">(Sayed \& Kailath, 2001)</a></sup>
: ([Sayed and Kailath 2001](#org0cb985f))
Author(s)
: Sayed, A. H., & Kailath, T.
@@ -17,5 +17,7 @@ Author(s)
Year
: 2001
# Bibliography
<a id="sayed01_survey_spect_factor_method"></a>Sayed, A. H., & Kailath, T., *A survey of spectral factorization methods*, Numerical Linear Algebra with Applications, *8(6-7)*, 467–496 (2001). http://dx.doi.org/10.1002/nla.250 [↩](#e71cc5e3ec879813f2344a6dce1ac11f)
## Bibliography {#bibliography}
<a id="org0cb985f"></a>Sayed, A. H., and T. Kailath. 2001. “A Survey of Spectral Factorization Methods.” _Numerical Linear Algebra with Applications_ 8 (6-7):467–96. <https://doi.org/10.1002/nla.250>.

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Reference
: <sup id="ee9f1b2ad5707e86bf7c26e8c325b324"><a class="reference-link" href="#schroeck01_compen_desig_linear_time_invar" title="Schroeck, Messner \&amp; McNab, On Compensator Design for Linear Time-Invariant Dual-Input Single-Output Systems, {IEEE/ASME Transactions on Mechatronics}, v(1), 50-57 (2001).">(Schroeck {\it et al.}, 2001)</a></sup>
: ([Schroeck, Messner, and McNab 2001](#orga714386))
Author(s)
: Schroeck, S., Messner, W., & McNab, R.
@@ -17,5 +17,7 @@ Author(s)
Year
: 2001
# Bibliography
<a class="bibtex-entry" id="schroeck01_compen_desig_linear_time_invar">Schroeck, S., Messner, W., & McNab, R., *On compensator design for linear time-invariant dual-input single-output systems*, IEEE/ASME Transactions on Mechatronics, *6(1)*, 50–57 (2001). http://dx.doi.org/10.1109/3516.914391</a> [↩](#ee9f1b2ad5707e86bf7c26e8c325b324)
## Bibliography {#bibliography}
<a id="orga714386"></a>Schroeck, S.J., W.C. Messner, and R.J. McNab. 2001. “On Compensator Design for Linear Time-Invariant Dual-Input Single-Output Systems.” _IEEE/ASME Transactions on Mechatronics_ 6 (1):50–57. <https://doi.org/10.1109/3516.914391>.

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@@ -8,7 +8,7 @@ Tags
: [Active Damping]({{< relref "active_damping" >}})
Reference
: <sup id="d5c1263eebe6caa1e91b078b620d72f1"><a class="reference-link" href="#souleille18_concep_activ_mount_space_applic" title="Souleille, Lampert, Lafarga, , Hellegouarch, Rondineau, Rodrigues, Gon\ccalo \&amp; Collette, A Concept of Active Mount for Space Applications, {CEAS Space Journal}, v(2), 157--165 (2018).">(Souleille {\it et al.}, 2018)</a></sup>
: ([Souleille et al. 2018](#org91c3531))
Author(s)
: Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gonccalo, & Collette, C.
@@ -23,10 +23,10 @@ This article discusses the use of Integral Force Feedback with amplified piezoel
## Single degree-of-freedom isolator {#single-degree-of-freedom-isolator}
Figure [1](#orgec40a2d) shows a picture of the amplified piezoelectric stack.
Figure [1](#org4fea547) shows a picture of the amplified piezoelectric stack.
The piezoelectric actuator is divided into two parts: one is used as an actuator, and the other one is used as a force sensor.
<a id="orgec40a2d"></a>
<a id="org4fea547"></a>
{{< figure src="/ox-hugo/souleille18_model_piezo.png" caption="Figure 1: Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator" >}}
@@ -61,36 +61,38 @@ and the control force is given by:
f = F\_s G(s) = F\_s \frac{g}{s}
\end{equation}
The effect of the controller are shown in Figure [2](#org656442f):
The effect of the controller are shown in Figure [2](#orgfc78016):
- the resonance peak is almost critically damped
- the passive isolation \\(\frac{x\_1}{w}\\) is not degraded at high frequencies
- the degradation of the compliance \\(\frac{x\_1}{F}\\) induced by feedback is limited at \\(\frac{1}{k\_1}\\)
- the fraction of the force transmitted to the payload that is measured by the force sensor is reduced at low frequencies
<a id="org656442f"></a>
<a id="orgfc78016"></a>
{{< figure src="/ox-hugo/souleille18_tf_iff_result.png" caption="Figure 2: Matrix of transfer functions from input (w, f, F) to output (Fs, x1) in open loop (blue curves) and closed loop (dashed red curves)" >}}
<a id="orgd1fa41a"></a>
<a id="org86440e0"></a>
{{< figure src="/ox-hugo/souleille18_root_locus.png" caption="Figure 3: Single DoF system. Comparison between the theoretical (solid curve) and the experimental (crosses) root-locus" >}}
## Flexible payload mounted on three isolators {#flexible-payload-mounted-on-three-isolators}
A heavy payload is mounted on a set of three isolators (Figure [4](#org59a9fbf)).
A heavy payload is mounted on a set of three isolators (Figure [4](#org2b1d225)).
The payload consists of two masses, connected through flexible blades such that the flexible resonance of the payload in the vertical direction is around 65Hz.
<a id="org59a9fbf"></a>
<a id="org2b1d225"></a>
{{< figure src="/ox-hugo/souleille18_setup_flexible_payload.png" caption="Figure 4: Right: picture of the experimental setup. It consists of a flexible payload mounted on a set of three isolators. Left: simplified sketch of the setup, showing only the vertical direction" >}}
As shown in Figure [5](#orgb30c1f0), both the suspension modes and the flexible modes of the payload can be critically damped.
As shown in Figure [5](#orge25f187), both the suspension modes and the flexible modes of the payload can be critically damped.
<a id="orgb30c1f0"></a>
<a id="orge25f187"></a>
{{< figure src="/ox-hugo/souleille18_result_damping_transmissibility.png" caption="Figure 5: Transmissibility between the table top \\(w\\) and \\(m\_1\\)" >}}
# Bibliography
<a class="bibtex-entry" id="souleille18_concep_activ_mount_space_applic">Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gon\ccalo, & Collette, C., *A concept of active mount for space applications*, CEAS Space Journal, *10(2)*, 157–165 (2018). </a> [↩](#d5c1263eebe6caa1e91b078b620d72f1)
## Bibliography {#bibliography}
<a id="org91c3531"></a>Souleille, Adrien, Thibault Lampert, V Lafarga, Sylvain Hellegouarch, Alan Rondineau, Gonçalo Rodrigues, and Christophe Collette. 2018. “A Concept of Active Mount for Space Applications.” _CEAS Space Journal_ 10 (2). Springer:157–65.

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: [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference
: <sup id="85f81ff678aabc195636437548e4234a"><a class="reference-link" href="#tang18_decen_vibrat_contr_voice_coil" title="Jie Tang, Dengqing Cao \&amp; Tianhu Yu, Decentralized Vibration Control of a Voice Coil Motor-Based Stewart Parallel Mechanism: Simulation and Experiments, {Proceedings of the Institution of Mechanical Engineers,
Part C: Journal of Mechanical Engineering Science}, v(1), 132-145 (2018).">(Jie Tang {\it et al.}, 2018)</a></sup>
: ([Tang, Cao, and Yu 2018](#org6d9be33))
Author(s)
: Tang, J., Cao, D., & Yu, T.
@@ -17,5 +16,7 @@ Author(s)
Year
: 2018
# Bibliography
<a class="bibtex-entry" id="tang18_decen_vibrat_contr_voice_coil">Tang, J., Cao, D., & Yu, T., *Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments*, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, *233(1)*, 132–145 (2018). http://dx.doi.org/10.1177/0954406218756941</a> [↩](#85f81ff678aabc195636437548e4234a)
## Bibliography {#bibliography}
<a id="org6d9be33"></a>Tang, Jie, Dengqing Cao, and Tianhu Yu. 2018. “Decentralized Vibration Control of a Voice Coil Motor-Based Stewart Parallel Mechanism: Simulation and Experiments.” _Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science_ 233 (1):132–45. <https://doi.org/10.1177/0954406218756941>.

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@@ -8,7 +8,7 @@ Tags
: [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system" >}})
Reference
: <sup id="1bccbe15e35ed02229afbc6528c5057e"><a class="reference-link" href="#wang12_autom_marker_full_field_hard" title="Jun Wang, Yu-chen Karen Chen, Qingxi Yuan, Andrei, Tkachuk, Can Erdonmez, Benjamin Hornberger, Michael \&amp; Feser, Automated Markerless Full Field Hard X-Ray Microscopic Tomography At Sub-50 Nm 3-dimension Spatial Resolution, {Applied Physics Letters}, v(14), 143107 (2012).">(Jun Wang {\it et al.}, 2012)</a></sup>
: ([Wang et al. 2012](#org72cf603))
Author(s)
: Wang, J., Chen, Y. K., Yuan, Q., Tkachuk, A., Erdonmez, C., Hornberger, B., & Feser, M.
@@ -25,5 +25,7 @@ There is a need for markerless nano-tomography
**Passive rotational run-out error system**:
It uses calibrated metrology disc and capacitive sensors
# Bibliography
<a class="bibtex-entry" id="wang12_autom_marker_full_field_hard">Wang, J., Chen, Y. K., Yuan, Q., Tkachuk, A., Erdonmez, C., Hornberger, B., & Feser, M., *Automated markerless full field hard x-ray microscopic tomography at sub-50 nm 3-dimension spatial resolution*, Applied Physics Letters, *100(14)*, 143107 (2012). http://dx.doi.org/10.1063/1.3701579</a> [↩](#1bccbe15e35ed02229afbc6528c5057e)
## Bibliography {#bibliography}
<a id="org72cf603"></a>Wang, Jun, Yu-chen Karen Chen, Qingxi Yuan, Andrei Tkachuk, Can Erdonmez, Benjamin Hornberger, and Michael Feser. 2012. “Automated Markerless Full Field Hard X-Ray Microscopic Tomography at Sub-50 Nm 3-Dimension Spatial Resolution.” _Applied Physics Letters_ 100 (14):143107. <https://doi.org/10.1063/1.3701579>.

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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference
: <sup id="db95fac7cd46c14e2b4f38e8ca4158fe"><a class="reference-link" href="#wang16_inves_activ_vibrat_isolat_stewar" title="Wang, Xie, Chen, Zhang \&amp; Zhiyi, Investigation on Active Vibration Isolation of a Stewart Platform With Piezoelectric Actuators, {Journal of Sound and Vibration}, v(), 1-19 (2016).">(Wang {\it et al.}, 2016)</a></sup>
: ([Wang et al. 2016](#org22df838))
Author(s)
: Wang, C., Xie, X., Chen, Y., & Zhang, Z.
@@ -25,7 +25,7 @@ Year
The model is compared with a Finite Element model and is shown to give the same results.
The proposed model is thus effective.
<a id="orgd3fa417"></a>
<a id="org0dd5327"></a>
{{< figure src="/ox-hugo/wang16_stewart_platform.png" caption="Figure 1: Stewart Platform" >}}
@@ -35,11 +35,11 @@ Combines:
- the FxLMS-based adaptive inverse control => suppress transmission of periodic vibrations
- direct feedback of integrated forces => dampen vibration of inherent modes and thus reduce random vibrations
Force Feedback (Figure [2](#org55d173d)).
Force Feedback (Figure [2](#org0b0c9ed)).
- the force sensor is mounted **between the base and the strut**
<a id="org55d173d"></a>
<a id="org0b0c9ed"></a>
{{< figure src="/ox-hugo/wang16_force_feedback.png" caption="Figure 2: Feedback of integrated forces in the platform" >}}
@@ -53,5 +53,7 @@ Sorts of HAC-LAC control:
- All 6 transfer function from actuator force to force sensors are almost the same (gain offset)
- Effectiveness of control methods are shown
# Bibliography
<a class="bibtex-entry" id="wang16_inves_activ_vibrat_isolat_stewar">Wang, C., Xie, X., Chen, Y., & Zhang, Z., *Investigation on active vibration isolation of a stewart platform with piezoelectric actuators*, Journal of Sound and Vibration, *383()*, 1–19 (2016). http://dx.doi.org/10.1016/j.jsv.2016.07.021</a> [↩](#db95fac7cd46c14e2b4f38e8ca4158fe)
## Bibliography {#bibliography}
<a id="org22df838"></a>Wang, Chaoxin, Xiling Xie, Yanhao Chen, and Zhiyi Zhang. 2016. “Investigation on Active Vibration Isolation of a Stewart Platform with Piezoelectric Actuators.” _Journal of Sound and Vibration_ 383 (November). Elsevier BV:1–19. <https://doi.org/10.1016/j.jsv.2016.07.021>.

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@@ -9,7 +9,7 @@ Tags
Reference
: <sup id="44caf201a37b1b3af63de65257785085"><a class="reference-link" href="#yun20_inves_two_stage_vibrat_suppr" title="Hai Yun, Lei Liu, Qing Li \&amp; Hongjie Yang, Investigation on Two-Stage Vibration Suppression and Precision Pointing for Space Optical Payloads, {Aerospace Science and Technology}, v(nil), 105543 (2020).">(Hai Yun {\it et al.}, 2020)</a></sup>
: ([Yun et al. 2020](#org63dfd15))
Author(s)
: Yun, H., Liu, L., Li, Q., & Yang, H.
@@ -17,5 +17,7 @@ Author(s)
Year
: 2020
# Bibliography
<a class="bibtex-entry" id="yun20_inves_two_stage_vibrat_suppr">Yun, H., Liu, L., Li, Q., & Yang, H., *Investigation on two-stage vibration suppression and precision pointing for space optical payloads*, Aerospace Science and Technology, *96(nil)*, 105543 (2020). http://dx.doi.org/10.1016/j.ast.2019.105543</a> [↩](#44caf201a37b1b3af63de65257785085)
## Bibliography {#bibliography}
<a id="org63dfd15"></a>Yun, Hai, Lei Liu, Qing Li, and Hongjie Yang. 2020. “Investigation on Two-Stage Vibration Suppression and Precision Pointing for Space Optical Payloads.” _Aerospace Science and Technology_ 96 (nil):105543. <https://doi.org/10.1016/j.ast.2019.105543>.

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@@ -8,7 +8,7 @@ Tags
: [Vibration Isolation]({{< relref "vibration_isolation" >}})
Reference
: <sup id="e9037e3bf20089c45ab77215406558ca"><a class="reference-link" href="#zuo04_elemen_system_desig_activ_passiv_vibrat_isolat" title="Zuo, Element and System Design for Active and Passive Vibration Isolation (2004).">(Zuo, 2004)</a></sup>
: ([Zuo 2004](#org21a244a))
Author(s)
: Zuo, L.
@@ -26,21 +26,23 @@ Year
> They found that coupling from flexible modes is much smaller than in soft active mounts in the load (force) feedback.
> Note that reaction force actuators can also work with soft mounts or hard mounts.
<a id="org0286cf1"></a>
<a id="org813c7b5"></a>
{{< figure src="/ox-hugo/zuo04_piezo_spring_series.png" caption="Figure 1: PZT actuator and spring in series" >}}
<a id="org679f77c"></a>
<a id="orgb0453c3"></a>
{{< figure src="/ox-hugo/zuo04_voice_coil_spring_parallel.png" caption="Figure 2: Voice coil actuator and spring in parallel" >}}
<a id="orged24ee6"></a>
<a id="orgc0f3c0e"></a>
{{< figure src="/ox-hugo/zuo04_piezo_plant.png" caption="Figure 3: Transmission from PZT voltage to geophone output" >}}
<a id="org9b75d10"></a>
<a id="org0739a0f"></a>
{{< figure src="/ox-hugo/zuo04_voice_coil_plant.png" caption="Figure 4: Transmission from voice coil voltage to geophone output" >}}
# Bibliography
<a class="bibtex-entry" id="zuo04_elemen_system_desig_activ_passiv_vibrat_isolat">Zuo, L., *Element and system design for active and passive vibration isolation* (2004). Massachusetts Institute of Technology.</a> [↩](#e9037e3bf20089c45ab77215406558ca)
## Bibliography {#bibliography}
<a id="org21a244a"></a>Zuo, Lei. 2004. “Element and System Design for Active and Passive Vibration Isolation.” Massachusetts Institute of Technology.