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mahd/implementation/submodel/endeffector/endeffector.emx

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  1. <?xml version="1.0" encoding="UTF-8"?>

  2. <Document>

  3.  <Model version="4.8" build="4.8.2.10124">

  4.   <Sidops><![CDATA[model 128 184

  5.  description '<Information>

  6.  <Description>

  7.     <Version>4.8</Version>

  8. <IsMainModel>0</IsMainModel>

  9.   <KeepParameterValues>False</KeepParameterValues>

  10.     <LibraryPath>C:\users\wouter\My Documents\studie\ma\mahd\implementation\submodel\endeffector\endeffector.emx</LibraryPath>

  11.   <TimeStamp>2020-7-6 14:39:32</TimeStamp>

  12. </Description>

  13. </Information>';

  14.  type Mainmodel

  15.  end;

  16.  implementation bg

  17.   submodels

  18.    endeffector 592 296

  19.     description '<Description>

  20.    <IsMainModel>1</IsMainModel>

  21.    <KeepParameterValues>True</KeepParameterValues>

  22.    <Version>4.8</Version>

  23.    <Description>Model generated by 3D-Mechanics Toolbox

  24. 	Original Filename: C:\users\wouter\My Documents\studie\ma\mahd\implementation\submodel\endeffector\endeffector.3dm</Description>

  25.    <LibraryPath>C:\users\wouter\My Documents\studie\ma\mahd\implementation\submodel\endeffector\endeffector.emx</LibraryPath>

  26.    <TimeStamp>2020-7-6 14:12:40</TimeStamp>

  27. </Description>';

  28.     type MechanicsModel

  29.      ports

  30.       signal out H_marker [4,4];

  31.       mechanical psi in marker2 [6,1];

  32.       signal out H_grippertop [4,4];

  33.       mechanical psi in grippertop2 [6,1];

  34.       signal out H_gripperbottom [4,4];

  35.       mechanical psi in gripperbottom [6,1];

  36.      restrictions

  37.       causality fixed in marker2;

  38.       causality fixed in grippertop2;

  39.       causality fixed in gripperbottom;

  40.     end;

  41.     icon bg bottom

  42.      figures

  43.       image 'C:\users\wouter\My Documents\studie\ma\mahd\implementation\submodel\endeffector\endeffectorIcon.png' 528 232 128 128;

  44.      terminals

  45.       marker2 592.5 296.5;

  46.       grippertop2 592.5 296.5;

  47.       gripperbottom 592.5 296.5;

  48.     end;

  49.     implementation eq

  50. // 20-sim 3D Mechanics Editor

  51. // C:\users\wouter\My Documents\studie\ma\mahd\implementation\submodel\endeffector\endeffector.3dm

  52. 

  53. variables

  54. 	real hidden World\AbsH[4,4];

  55. 	real hidden World\mass_x_I[6,6];

  56. 	real hidden holderWeld\ConnectionPoint1\AbsH[4,4];

  57. 	real hidden holderWeld\AbsH[4,4];

  58. 	real hidden holderWeld\ConnectionPoint2\AbsH[4,4];

  59. 	real hidden holder\AbsH[4,4];

  60. 	real hidden holder\mass_x_I[6,6];

  61. 	real hidden markerFree\ConnectionPoint1\AbsH[4,4];

  62. 	real hidden markerFree\AbsH[4,4];

  63. 	real hidden markerFree\RelH[4,4];

  64. 	real hidden markerFree\rotationInitial[4,4];

  65. 	real markerFree\quat[4];

  66. 	real markerFree\quatDot[4];

  67. 	real hidden markerFree\quatInitial[4];

  68. 	real markerFree\QOmega[4,4];

  69. 	real markerFree\vgen[6];

  70. 	real markerFree\x[3];

  71. 	real markerFree\v[3];

  72. 	real markerFree\vel[3];

  73. 	real markerFree_Rot[4,4];

  74. 	real hidden markerFree\ConnectionPoint2\AbsH[4,4];

  75. 	real hidden marker\AbsH[4,4];

  76. 	real hidden marker\mass_x_I[6,6];

  77. 	real hidden H_marker\ConnectionPoint1\AbsH[4,4];

  78. 	real hidden marker2\ConnectionPoint1\AbsH[4,4];

  79. 	real hidden grippertopFree\ConnectionPoint1\AbsH[4,4];

  80. 	real hidden grippertopFree\AbsH[4,4];

  81. 	real hidden grippertopFree\RelH[4,4];

  82. 	real hidden grippertopFree\rotationInitial[4,4];

  83. 	real grippertopFree\quat[4];

  84. 	real grippertopFree\quatDot[4];

  85. 	real hidden grippertopFree\quatInitial[4];

  86. 	real grippertopFree\QOmega[4,4];

  87. 	real grippertopFree\vgen[6];

  88. 	real grippertopFree\x[3];

  89. 	real grippertopFree\v[3];

  90. 	real grippertopFree\vel[3];

  91. 	real grippertopFree_Rot[4,4];

  92. 	real hidden grippertopFree\ConnectionPoint2\AbsH[4,4];

  93. 	real hidden grippertop\AbsH[4,4];

  94. 	real hidden grippertop\mass_x_I[6,6];

  95. 	real hidden FreeJoint1\ConnectionPoint1\AbsH[4,4];

  96. 	real hidden H_grippertop\ConnectionPoint1\AbsH[4,4];

  97. 	real hidden grippertop2\ConnectionPoint1\AbsH[4,4];

  98. 	real hidden gripperbaseFree\ConnectionPoint1\AbsH[4,4];

  99. 	real hidden gripperbaseFree\AbsH[4,4];

  100. 	real hidden gripperbaseFree\RelH[4,4];

  101. 	real hidden gripperbaseFree\rotationInitial[4,4];

  102. 	real gripperbaseFree\quat[4];

  103. 	real gripperbaseFree\quatDot[4];

  104. 	real hidden gripperbaseFree\quatInitial[4];

  105. 	real gripperbaseFree\QOmega[4,4];

  106. 	real gripperbaseFree\vgen[6];

  107. 	real gripperbaseFree\x[3];

  108. 	real gripperbaseFree\v[3];

  109. 	real gripperbaseFree\vel[3];

  110. 	real gripperbaseFree_Rot[4,4];

  111. 	real hidden gripperbaseFree\ConnectionPoint2\AbsH[4,4];

  112. 	real hidden gripperbase\AbsH[4,4];

  113. 	real hidden gripperbase\mass_x_I[6,6];

  114. 	real hidden FreeJoint1\ConnectionPoint2\AbsH[4,4];

  115. 	real hidden H_gripperbottom\ConnectionPoint1\AbsH[4,4];

  116. 	real hidden gripperbottom\ConnectionPoint1\AbsH[4,4];

  117. 	real v[18];

  118. 	real P[18];

  119. 	real PDot[18];

  120. 	real PDotBodies[18];

  121. 	real hidden AdjX2[6,6];

  122. 	real hidden AdjX2_T[6,6];

  123. 	real hidden adjAdjX2_1[6,6];

  124. 	real hidden adjAdjX2_2[6,6];

  125. 	real hidden adjAdjX2_3[6,6];

  126. 	real hidden adjAdjX2_4[6,6];

  127. 	real hidden adjAdjX2_5[6,6];

  128. 	real hidden adjAdjX2_6[6,6];

  129. 	real hidden AdjX3[6,6];

  130. 	real hidden AdjX3_T[6,6];

  131. 	real hidden adjAdjX3_1[6,6];

  132. 	real hidden adjAdjX3_2[6,6];

  133. 	real hidden adjAdjX3_3[6,6];

  134. 	real hidden adjAdjX3_4[6,6];

  135. 	real hidden adjAdjX3_5[6,6];

  136. 	real hidden adjAdjX3_6[6,6];

  137. 	real hidden AdjX4[6,6];

  138. 	real hidden AdjX4_T[6,6];

  139. 	real hidden adjAdjX4_1[6,6];

  140. 	real hidden adjAdjX4_2[6,6];

  141. 	real hidden adjAdjX4_3[6,6];

  142. 	real hidden adjAdjX4_4[6,6];

  143. 	real hidden adjAdjX4_5[6,6];

  144. 	real hidden adjAdjX4_6[6,6];

  145. 	real hidden J1[6,18];

  146. 	real hidden J2[6,18];

  147. 	real hidden J3[6,18];

  148. 	real hidden J4[6,18];

  149. 	real hidden T1_00[6];

  150. 	real hidden T1_00T[1,6];

  151. 	real hidden T2_00[6];

  152. 	real hidden T2_00T[1,6];

  153. 	real hidden T3_00[6];

  154. 	real hidden T3_00T[1,6];

  155. 	real hidden T4_00[6];

  156. 	real hidden T4_00T[1,6];

  157. 	real hidden M1[6,6];

  158. 	real hidden AdjInv1[6,6];

  159. 	real hidden TM1[1,6];

  160. 	real hidden M2[6,6];

  161. 	real hidden AdjInv2[6,6];

  162. 	real hidden TM2[1,6];

  163. 	real hidden M3[6,6];

  164. 	real hidden AdjInv3[6,6];

  165. 	real hidden TM3[1,6];

  166. 	real hidden M4[6,6];

  167. 	real hidden AdjInv4[6,6];

  168. 	real hidden TM4[1,6];

  169. 	real MassMatrix[18,18];

  170. 	real hidden M2_2[6,6];

  171. 	real hidden M3_3[6,6];

  172. 	real hidden M4_4[6,6];

  173. 	real hidden wrenchGrav2[1,6];

  174. 	real hidden wrenchGrav3[1,6];

  175. 	real hidden wrenchGrav4[1,6];

  176. 	real FreeJoint1\ConnectionPoint1\invAdjointH[6,6];

  177. 	real FreeJoint1\ConnectionPoint1\AbsHinverse[4,4];

  178. 	real FreeJoint1\ConnectionPoint2\invAdjointH[6,6];

  179. 	real FreeJoint1\ConnectionPoint2\AbsHinverse[4,4];

  180. 	real FreeJoint1\ConnectionPoint1_effort[1,6];

  181. 	real FreeJoint1\ConnectionPoint1_flow[6];

  182. 	real FreeJoint1\ConnectionPoint2_effort[1,6];

  183. 	real FreeJoint1\ConnectionPoint2_flow[6];

  184. 	real FreeJoint1_relH[4,4];

  185. 	real FreeJoint1_relT[6];

  186. 	real FreeJoint1_relW[1,6];

  187. 	real FreeJoint1_f1;

  188. 	real FreeJoint1_e1;

  189. 	real FreeJoint1_f2;

  190. 	real FreeJoint1_e2;

  191. 	real FreeJoint1_f3;

  192. 	real FreeJoint1_e3;

  193. 	real FreeJoint1_f4;

  194. 	real FreeJoint1_e4;

  195. 	real FreeJoint1_f5;

  196. 	real FreeJoint1_e5;

  197. 	real FreeJoint1_f6;

  198. 	real FreeJoint1_e6;

  199. 	real FreeJoint1_EulerXZY[3];

  200. 	real FreeJoint1_EulerYXZ[3];

  201. 	real FreeJoint1\SpringForce;

  202. 	real FreeJoint1\DampingForce;

  203. 	real markerFree\Bk[6,6];

  204. 	real hidden markerFree\skewP4to6[3,3];

  205. 	real TMSum2[1,6];

  206. 	real grippertopFree\Bk[6,6];

  207. 	real hidden grippertopFree\skewP4to6[3,3];

  208. 	real TMSum3[1,6];

  209. 	real gripperbaseFree\Bk[6,6];

  210. 	real hidden gripperbaseFree\skewP4to6[3,3];

  211. 	real TMSum4[1,6];

  212. parameters

  213. 	real hidden World\H[4,4] = [

  214. 			1, 0, 0, 0;

  215. 			0, 1, 0, 0;

  216. 			0, 0, 1, 0;

  217. 			0, 0, 0, 1];

  218. 	real hidden World\I[6,6] = [

  219. 			0.1, 0, 0, 0, 0, 0;

  220. 			0, 0.1, 0, 0, 0, 0;

  221. 			0, 0, 0.1, 0, 0, 0;

  222. 			0, 0, 0, 1, 0, 0;

  223. 			0, 0, 0, 0, 1, 0;

  224. 			0, 0, 0, 0, 0, 1];

  225. 	real World\mass = 1;

  226. 	real hidden holderWeld\ConnectionPoint1\RelH[4,4] = [

  227. 			1, 0, 0, 0;

  228. 			0, 1, 0, 0.11;

  229. 			0, 0, 1, -0.0088;

  230. 			0, 0, 0, 1];

  231. 	real hidden holder\RelH[4,4] = [

  232. 			1, 0, 0, 0;

  233. 			0, 1, 0, 0;

  234. 			0, 0, 1, 0;

  235. 			0, 0, 0, 1];

  236. 	real hidden holder\I[6,6] = [

  237. 			0.1, 0, 0, 0, 0, 0;

  238. 			0, 0.1, 0, 0, 0, 0;

  239. 			0, 0, 0.1, 0, 0, 0;

  240. 			0, 0, 0, 1, 0, 0;

  241. 			0, 0, 0, 0, 1, 0;

  242. 			0, 0, 0, 0, 0, 1];

  243. 	real holder\mass = 1;

  244. 	real hidden markerFree\ConnectionPoint1\RelH[4,4] = [

  245. 			1, 0, 0, 0;

  246. 			0, 1, 0, 0;

  247. 			0, 0, 1, 0;

  248. 			0, 0, 0, 1];

  249. 	real markerFree\EulerXYZInitial[3] = [1.5707963267949; 0; -0];

  250. 	real hidden markerFree\xInitial[3] = [0; 0.1; 0];

  251. 	real hidden marker\RelH[4,4] = [

  252. 			1, 0, 0, 0;

  253. 			0, 1, 0, 0;

  254. 			0, 0, 1, 0;

  255. 			0, 0, 0, 1];

  256. 	real hidden marker\I[6,6] = [

  257. 			0.00163636363636364, 0, 0, 0, 0, 0;

  258. 			0, 2.6645e-005, 0, 0, 0, 0;

  259. 			0, 0, 0.00163636363636364, 0, 0, 0;

  260. 			0, 0, 0, 1, 0, 0;

  261. 			0, 0, 0, 0, 1, 0;

  262. 			0, 0, 0, 0, 0, 1];

  263. 	real marker\mass = 0.011;

  264. 	real hidden H_marker\ConnectionPoint1\RelH[4,4] = [

  265. 			1, 0, 0, 0;

  266. 			0, 1, 0, 0;

  267. 			0, 0, 1, 0;

  268. 			0, 0, 0, 1];

  269. 	real hidden marker2\ConnectionPoint1\RelH[4,4] = [

  270. 			1, 0, 0, 0;

  271. 			0, 1, 0, 0;

  272. 			0, 0, 1, 0;

  273. 			0, 0, 0, 1];

  274. 	real hidden grippertopFree\ConnectionPoint1\RelH[4,4] = [

  275. 			1, 0, 0, 0;

  276. 			0, 1, 0, 0;

  277. 			0, 0, 1, 0;

  278. 			0, 0, 0, 1];

  279. 	real grippertopFree\EulerXYZInitial[3] = [-0; 0; -0];

  280. 	real hidden grippertopFree\xInitial[3] = [0; 0.11; 0.015];

  281. 	real hidden grippertop\RelH[4,4] = [

  282. 			1, 0, 0, 0;

  283. 			0, 1, 0, 0;

  284. 			0, 0, 1, 0;

  285. 			0, 0, 0, 1];

  286. 	real hidden grippertop\I[6,6] = [

  287. 			0.1, 0, 0, 0, 0, 0;

  288. 			0, 0.1, 0, 0, 0, 0;

  289. 			0, 0, 0.1, 0, 0, 0;

  290. 			0, 0, 0, 1, 0, 0;

  291. 			0, 0, 0, 0, 1, 0;

  292. 			0, 0, 0, 0, 0, 1];

  293. 	real grippertop\mass = 1;

  294. 	real hidden FreeJoint1\ConnectionPoint1\RelH[4,4] = [

  295. 			1, 0, 0, 0.05;

  296. 			0, 1, 0, 0;

  297. 			0, 0, 1, 0;

  298. 			0, 0, 0, 1];

  299. 	real hidden H_grippertop\ConnectionPoint1\RelH[4,4] = [

  300. 			1, 0, 0, 0;

  301. 			0, 1, 0, 0;

  302. 			0, 0, 1, 0;

  303. 			0, 0, 0, 1];

  304. 	real hidden grippertop2\ConnectionPoint1\RelH[4,4] = [

  305. 			1, 0, 0, 0;

  306. 			0, 1, 0, 0;

  307. 			0, 0, 1, 0;

  308. 			0, 0, 0, 1];

  309. 	real hidden gripperbaseFree\ConnectionPoint1\RelH[4,4] = [

  310. 			1, 0, 0, 0;

  311. 			0, 1, 0, 0;

  312. 			0, 0, 1, 0;

  313. 			0, 0, 0, 1];

  314. 	real gripperbaseFree\EulerXYZInitial[3] = [-0; 0; -0];

  315. 	real hidden gripperbaseFree\xInitial[3] = [0; 0.11; 0];

  316. 	real hidden gripperbase\RelH[4,4] = [

  317. 			1, 0, 0, 0;

  318. 			0, 1, 0, 0;

  319. 			0, 0, 1, 0;

  320. 			0, 0, 0, 1];

  321. 	real hidden gripperbase\I[6,6] = [

  322. 			0.02, 0, 0, 0, 0, 0;

  323. 			0, 0.02, 0, 0, 0, 0;

  324. 			0, 0, 0.08, 0, 0, 0;

  325. 			0, 0, 0, 1, 0, 0;

  326. 			0, 0, 0, 0, 1, 0;

  327. 			0, 0, 0, 0, 0, 1];

  328. 	real gripperbase\mass = 0.005;

  329. 	real hidden FreeJoint1\ConnectionPoint2\RelH[4,4] = [

  330. 			1, 0, 0, 0.05;

  331. 			0, 1, 0, 0;

  332. 			0, 0, 1, 0.015;

  333. 			0, 0, 0, 1];

  334. 	real hidden H_gripperbottom\ConnectionPoint1\RelH[4,4] = [

  335. 			1, 0, 0, 0;

  336. 			0, 1, 0, 0;

  337. 			0, 0, 1, 0;

  338. 			0, 0, 0, 1];

  339. 	real hidden gripperbottom\ConnectionPoint1\RelH[4,4] = [

  340. 			1, 0, 0, 0;

  341. 			0, 1, 0, 0;

  342. 			0, 0, 1, 0;

  343. 			0, 0, 0, 1];

  344. 	real gravity[3] = [0; 0; -9.81];

  345. 	real constraintRotSpringK = 10000;

  346. 	real constraintRotDamperD = 100;

  347. 	real FreeJoint1\Spring = 1;

  348. 	real FreeJoint1\Damping = 1;

  349. 	real constraintTransSpringK = 100000;

  350. 	real constraintTransDamperD = 100;

  351. 	real hidden PDotInitial[18] = [0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0];

  352. initialequations

  353. 	markerFree\rotationInitial = dll ('EulerAngles.dll', 'HMatrixFromEulXYZr', markerFree\EulerXYZInitial);

  354. 	markerFree\quatInitial = dll ('EulerAngles.dll', 'QuaternionFromHMatrix', markerFree\rotationInitial);

  355. 	markerFree\RelH[4, 1:3] = 0;

  356. 	markerFree\RelH[4, 4] = 1;

  357. 	grippertopFree\rotationInitial = dll ('EulerAngles.dll', 'HMatrixFromEulXYZr', grippertopFree\EulerXYZInitial);

  358. 	grippertopFree\quatInitial = dll ('EulerAngles.dll', 'QuaternionFromHMatrix', grippertopFree\rotationInitial);

  359. 	grippertopFree\RelH[4, 1:3] = 0;

  360. 	grippertopFree\RelH[4, 4] = 1;

  361. 	gripperbaseFree\rotationInitial = dll ('EulerAngles.dll', 'HMatrixFromEulXYZr', gripperbaseFree\EulerXYZInitial);

  362. 	gripperbaseFree\quatInitial = dll ('EulerAngles.dll', 'QuaternionFromHMatrix', gripperbaseFree\rotationInitial);

  363. 	gripperbaseFree\RelH[4, 1:3] = 0;

  364. 	gripperbaseFree\RelH[4, 4] = 1;

  365. 	J1[1:6, 1:6] = 0;

  366. 	J1[1:6, 7:12] = 0;

  367. 	J1[1:6, 13:18] = 0;

  368. 	J2[1:6, 7:12] = 0;

  369. 	J2[1:6, 13:18] = 0;

  370. 	J3[1:6, 1:6] = 0;

  371. 	J3[1:6, 13:18] = 0;

  372. 	J4[1:6, 1:6] = 0;

  373. 	J4[1:6, 7:12] = 0;

  374. 	MassMatrix[1:6, 7:12] = 0;

  375. 	MassMatrix[1:6, 13:18] = 0;

  376. 	MassMatrix[7:12, 1:6] = 0;

  377. 	MassMatrix[7:12, 13:18] = 0;

  378. 	MassMatrix[13:18, 1:6] = 0;

  379. 	MassMatrix[13:18, 7:12] = 0;

  380. 	markerFree\Bk[4:6, 4:6] = 0;

  381. 	grippertopFree\Bk[4:6, 4:6] = 0;

  382. 	gripperbaseFree\Bk[4:6, 4:6] = 0;

  383. equations

  384. 	World\AbsH = World\H;

  385. 	World\mass_x_I = World\mass * World\I;

  386. 	holderWeld\ConnectionPoint1\AbsH = multiplyH (World\AbsH, holderWeld\ConnectionPoint1\RelH);

  387. 	holderWeld\AbsH = holderWeld\ConnectionPoint1\AbsH;

  388. 	holderWeld\ConnectionPoint2\AbsH = holderWeld\AbsH;

  389. 	holder\AbsH = multiplyH (holderWeld\ConnectionPoint2\AbsH, holder\RelH);

  390. 	holder\mass_x_I = holder\mass * holder\I;

  391. 	markerFree\ConnectionPoint1\AbsH = multiplyH (World\AbsH, markerFree\ConnectionPoint1\RelH);

  392. 	markerFree\QOmega = [0, -markerFree\vgen[3], markerFree\vgen[2], -markerFree\vgen[1];

  393. 				markerFree\vgen[3], 0, -markerFree\vgen[1], -markerFree\vgen[2];

  394. 				-markerFree\vgen[2], markerFree\vgen[1], 0, -markerFree\vgen[3];

  395. 				markerFree\vgen[1], markerFree\vgen[2], markerFree\vgen[3], 0];

  396. 	markerFree\quat = int (markerFree\quatDot) + markerFree\quatInitial;

  397. 	markerFree\quatDot = 0.5 * (markerFree\QOmega * markerFree\quat);

  398. 	markerFree\vel = markerFree\vgen[4:6];

  399. 	markerFree\v = skew (markerFree\vgen[1:3]) * markerFree\x + markerFree\vel;

  400. 	markerFree\x = int (markerFree\v) + markerFree\xInitial;

  401. 	markerFree_Rot = dll ('EulerAngles.dll', 'HMatrixFromQuaternion', markerFree\quat);

  402. 	markerFree\RelH[1:3, 1:3] = markerFree_Rot[1:3, 1:3];

  403. 	markerFree\RelH[1:3, 4] = markerFree\x;

  404. 	markerFree\AbsH = multiplyH (markerFree\ConnectionPoint1\AbsH, markerFree\RelH);

  405. 	markerFree\ConnectionPoint2\AbsH = markerFree\AbsH;

  406. 	marker\AbsH = multiplyH (markerFree\ConnectionPoint2\AbsH, marker\RelH);

  407. 	marker\mass_x_I = marker\mass * marker\I;

  408. 	H_marker\ConnectionPoint1\AbsH = multiplyH (marker\AbsH, H_marker\ConnectionPoint1\RelH);

  409. 	marker2\ConnectionPoint1\AbsH = multiplyH (marker\AbsH, marker2\ConnectionPoint1\RelH);

  410. 	grippertopFree\ConnectionPoint1\AbsH = multiplyH (World\AbsH, grippertopFree\ConnectionPoint1\RelH);

  411. 	grippertopFree\QOmega = [0, -grippertopFree\vgen[3], grippertopFree\vgen[2], -grippertopFree\vgen[1];

  412. 				grippertopFree\vgen[3], 0, -grippertopFree\vgen[1], -grippertopFree\vgen[2];

  413. 				-grippertopFree\vgen[2], grippertopFree\vgen[1], 0, -grippertopFree\vgen[3];

  414. 				grippertopFree\vgen[1], grippertopFree\vgen[2], grippertopFree\vgen[3], 0];

  415. 	grippertopFree\quat = int (grippertopFree\quatDot) + grippertopFree\quatInitial;

  416. 	grippertopFree\quatDot = 0.5 * (grippertopFree\QOmega * grippertopFree\quat);

  417. 	grippertopFree\vel = grippertopFree\vgen[4:6];

  418. 	grippertopFree\v = skew (grippertopFree\vgen[1:3]) * grippertopFree\x + grippertopFree\vel;

  419. 	grippertopFree\x = int (grippertopFree\v) + grippertopFree\xInitial;

  420. 	grippertopFree_Rot = dll ('EulerAngles.dll', 'HMatrixFromQuaternion', grippertopFree\quat);

  421. 	grippertopFree\RelH[1:3, 1:3] = grippertopFree_Rot[1:3, 1:3];

  422. 	grippertopFree\RelH[1:3, 4] = grippertopFree\x;

  423. 	grippertopFree\AbsH = multiplyH (grippertopFree\ConnectionPoint1\AbsH, grippertopFree\RelH);

  424. 	grippertopFree\ConnectionPoint2\AbsH = grippertopFree\AbsH;

  425. 	grippertop\AbsH = multiplyH (grippertopFree\ConnectionPoint2\AbsH, grippertop\RelH);

  426. 	grippertop\mass_x_I = grippertop\mass * grippertop\I;

  427. 	FreeJoint1\ConnectionPoint1\AbsH = multiplyH (grippertop\AbsH, FreeJoint1\ConnectionPoint1\RelH);

  428. 	H_grippertop\ConnectionPoint1\AbsH = multiplyH (grippertop\AbsH, H_grippertop\ConnectionPoint1\RelH);

  429. 	grippertop2\ConnectionPoint1\AbsH = multiplyH (grippertop\AbsH, grippertop2\ConnectionPoint1\RelH);

  430. 	gripperbaseFree\ConnectionPoint1\AbsH = multiplyH (World\AbsH, gripperbaseFree\ConnectionPoint1\RelH);

  431. 	gripperbaseFree\QOmega = [0, -gripperbaseFree\vgen[3], gripperbaseFree\vgen[2], -gripperbaseFree\vgen[1];

  432. 				gripperbaseFree\vgen[3], 0, -gripperbaseFree\vgen[1], -gripperbaseFree\vgen[2];

  433. 				-gripperbaseFree\vgen[2], gripperbaseFree\vgen[1], 0, -gripperbaseFree\vgen[3];

  434. 				gripperbaseFree\vgen[1], gripperbaseFree\vgen[2], gripperbaseFree\vgen[3], 0];

  435. 	gripperbaseFree\quat = int (gripperbaseFree\quatDot) + gripperbaseFree\quatInitial;

  436. 	gripperbaseFree\quatDot = 0.5 * (gripperbaseFree\QOmega * gripperbaseFree\quat);

  437. 	gripperbaseFree\vel = gripperbaseFree\vgen[4:6];

  438. 	gripperbaseFree\v = skew (gripperbaseFree\vgen[1:3]) * gripperbaseFree\x + gripperbaseFree\vel;

  439. 	gripperbaseFree\x = int (gripperbaseFree\v) + gripperbaseFree\xInitial;

  440. 	gripperbaseFree_Rot = dll ('EulerAngles.dll', 'HMatrixFromQuaternion', gripperbaseFree\quat);

  441. 	gripperbaseFree\RelH[1:3, 1:3] = gripperbaseFree_Rot[1:3, 1:3];

  442. 	gripperbaseFree\RelH[1:3, 4] = gripperbaseFree\x;

  443. 	gripperbaseFree\AbsH = multiplyH (gripperbaseFree\ConnectionPoint1\AbsH, gripperbaseFree\RelH);

  444. 	gripperbaseFree\ConnectionPoint2\AbsH = gripperbaseFree\AbsH;

  445. 	gripperbase\AbsH = multiplyH (gripperbaseFree\ConnectionPoint2\AbsH, gripperbase\RelH);

  446. 	gripperbase\mass_x_I = gripperbase\mass * gripperbase\I;

  447. 	FreeJoint1\ConnectionPoint2\AbsH = multiplyH (gripperbase\AbsH, FreeJoint1\ConnectionPoint2\RelH);

  448. 	H_gripperbottom\ConnectionPoint1\AbsH = multiplyH (gripperbase\AbsH, H_gripperbottom\ConnectionPoint1\RelH);

  449. 	gripperbottom\ConnectionPoint1\AbsH = multiplyH (gripperbase\AbsH, gripperbottom\ConnectionPoint1\RelH);

  450. 	AdjX2 = Adjoint (markerFree\ConnectionPoint1\AbsH);

  451. 	AdjX2_T = transpose (AdjX2);

  452. 	adjAdjX2_1 = adjoint (AdjX2[1:6, 1]);

  453. 	adjAdjX2_2 = adjoint (AdjX2[1:6, 2]);

  454. 	adjAdjX2_3 = adjoint (AdjX2[1:6, 3]);

  455. 	adjAdjX2_4 = adjoint (AdjX2[1:6, 4]);

  456. 	adjAdjX2_5 = adjoint (AdjX2[1:6, 5]);

  457. 	adjAdjX2_6 = adjoint (AdjX2[1:6, 6]);

  458. 	AdjX3 = Adjoint (grippertopFree\ConnectionPoint1\AbsH);

  459. 	AdjX3_T = transpose (AdjX3);

  460. 	adjAdjX3_1 = adjoint (AdjX3[1:6, 1]);

  461. 	adjAdjX3_2 = adjoint (AdjX3[1:6, 2]);

  462. 	adjAdjX3_3 = adjoint (AdjX3[1:6, 3]);

  463. 	adjAdjX3_4 = adjoint (AdjX3[1:6, 4]);

  464. 	adjAdjX3_5 = adjoint (AdjX3[1:6, 5]);

  465. 	adjAdjX3_6 = adjoint (AdjX3[1:6, 6]);

  466. 	AdjX4 = Adjoint (gripperbaseFree\ConnectionPoint1\AbsH);

  467. 	AdjX4_T = transpose (AdjX4);

  468. 	adjAdjX4_1 = adjoint (AdjX4[1:6, 1]);

  469. 	adjAdjX4_2 = adjoint (AdjX4[1:6, 2]);

  470. 	adjAdjX4_3 = adjoint (AdjX4[1:6, 3]);

  471. 	adjAdjX4_4 = adjoint (AdjX4[1:6, 4]);

  472. 	adjAdjX4_5 = adjoint (AdjX4[1:6, 5]);

  473. 	adjAdjX4_6 = adjoint (AdjX4[1:6, 6]);

  474. 	J2[1:6, 1:6] = AdjX2;

  475. 	J3[1:6, 7:12] = AdjX3;

  476. 	J4[1:6, 13:18] = AdjX4;

  477. 	T1_00 = J1 * v;

  478. 	T1_00T = transpose (T1_00);

  479. 	T2_00 = J2 * v;

  480. 	T2_00T = transpose (T2_00);

  481. 	T3_00 = J3 * v;

  482. 	T3_00T = transpose (T3_00);

  483. 	T4_00 = J4 * v;

  484. 	T4_00T = transpose (T4_00);

  485. 	AdjInv1 = Adjoint (inverseH (holder\AbsH));

  486. 	M1 = transpose (AdjInv1) * holder\mass_x_I * AdjInv1;

  487. 	TM1 = T1_00T * M1;

  488. 	AdjInv2 = Adjoint (inverseH (marker\AbsH));

  489. 	M2 = transpose (AdjInv2) * marker\mass_x_I * AdjInv2;

  490. 	TM2 = T2_00T * M2;

  491. 	AdjInv3 = Adjoint (inverseH (grippertop\AbsH));

  492. 	M3 = transpose (AdjInv3) * grippertop\mass_x_I * AdjInv3;

  493. 	TM3 = T3_00T * M3;

  494. 	AdjInv4 = Adjoint (inverseH (gripperbase\AbsH));

  495. 	M4 = transpose (AdjInv4) * gripperbase\mass_x_I * AdjInv4;

  496. 	TM4 = T4_00T * M4;

  497. 	M2_2 = AdjX2_T * (M2 * AdjX2);

  498. 	M3_3 = AdjX3_T * (M3 * AdjX3);

  499. 	M4_4 = AdjX4_T * (M4 * AdjX4);

  500. 	MassMatrix[1:6, 1:6] = M2_2;

  501. 	MassMatrix[7:12, 7:12] = M3_3;

  502. 	MassMatrix[13:18, 13:18] = M4_4;

  503. 	wrenchGrav2 = marker\mass * [gravity[3] * marker\AbsH[2, 4] - gravity[2] * marker\AbsH[3, 4], gravity[1] * marker\AbsH[3, 4] - gravity[3] * marker\AbsH[1, 4], gravity[2] * marker\AbsH[1, 4] - gravity[1] * marker\AbsH[2, 4], gravity[1], gravity[2], gravity[3]];

  504. 	wrenchGrav3 = grippertop\mass * [gravity[3] * grippertop\AbsH[2, 4] - gravity[2] * grippertop\AbsH[3, 4], gravity[1] * grippertop\AbsH[3, 4] - gravity[3] * grippertop\AbsH[1, 4], gravity[2] * grippertop\AbsH[1, 4] - gravity[1] * grippertop\AbsH[2, 4], gravity[1], gravity[2], gravity[3]];

  505. 	wrenchGrav4 = gripperbase\mass * [gravity[3] * gripperbase\AbsH[2, 4] - gravity[2] * gripperbase\AbsH[3, 4], gravity[1] * gripperbase\AbsH[3, 4] - gravity[3] * gripperbase\AbsH[1, 4], gravity[2] * gripperbase\AbsH[1, 4] - gravity[1] * gripperbase\AbsH[2, 4], gravity[1], gravity[2], gravity[3]];

  506. 	H_marker = H_marker\ConnectionPoint1\AbsH;

  507. 	marker2.f = T2_00;

  508. 	H_grippertop = H_grippertop\ConnectionPoint1\AbsH;

  509. 	grippertop2.f = T3_00;

  510. 	H_gripperbottom = H_gripperbottom\ConnectionPoint1\AbsH;

  511. 	gripperbottom.f = T4_00;

  512. 	FreeJoint1\ConnectionPoint1\AbsHinverse = inverseH (FreeJoint1\ConnectionPoint1\AbsH);

  513. 	FreeJoint1\ConnectionPoint1\invAdjointH = Adjoint (FreeJoint1\ConnectionPoint1\AbsHinverse);

  514. 	FreeJoint1\ConnectionPoint2\AbsHinverse = inverseH (FreeJoint1\ConnectionPoint2\AbsH);

  515. 	FreeJoint1\ConnectionPoint2\invAdjointH = Adjoint (FreeJoint1\ConnectionPoint2\AbsHinverse);

  516. 	FreeJoint1\ConnectionPoint1_flow = FreeJoint1\ConnectionPoint1\invAdjointH * T3_00;

  517. 	FreeJoint1\ConnectionPoint2_flow = FreeJoint1\ConnectionPoint2\invAdjointH * T4_00;

  518. 	FreeJoint1_relH = multiplyH (inverseH (FreeJoint1\ConnectionPoint1\AbsH), FreeJoint1\ConnectionPoint2\AbsH);

  519. 	FreeJoint1_relT = Adjoint (FreeJoint1_relH) * FreeJoint1\ConnectionPoint2_flow - FreeJoint1\ConnectionPoint1_flow;

  520. 	[FreeJoint1_f1;

  521. 				FreeJoint1_f2;

  522. 				FreeJoint1_f3;

  523. 				FreeJoint1_f4;

  524. 				FreeJoint1_f5;

  525. 				FreeJoint1_f6] = FreeJoint1_relT;

  526. 	FreeJoint1_EulerXZY = dll ('EulerAngles.dll', 'EulXZYrFromHMatrix', FreeJoint1_relH);

  527. 	FreeJoint1_e1 = -constraintRotSpringK * FreeJoint1_EulerXZY[1] - constraintRotDamperD * FreeJoint1_f1;

  528. 	FreeJoint1_EulerYXZ = dll ('EulerAngles.dll', 'EulYXZrFromHMatrix', FreeJoint1_relH);

  529. 	FreeJoint1\SpringForce = -(FreeJoint1_EulerYXZ[1] * FreeJoint1\Spring);

  530. 	FreeJoint1\DampingForce = -(FreeJoint1_f2 * FreeJoint1\Damping);

  531. 	FreeJoint1_e2 = FreeJoint1\SpringForce + FreeJoint1\DampingForce;

  532. 	FreeJoint1_e3 = -constraintRotSpringK * FreeJoint1_EulerXZY[2] - constraintRotDamperD * FreeJoint1_f3;

  533. 	FreeJoint1_e4 = -constraintTransSpringK * FreeJoint1_relH[1, 4] - constraintTransDamperD * FreeJoint1_f4;

  534. 	FreeJoint1_e5 = -constraintTransSpringK * FreeJoint1_relH[2, 4] - constraintTransDamperD * FreeJoint1_f5;

  535. 	FreeJoint1_e6 = -constraintTransSpringK * FreeJoint1_relH[3, 4] - constraintTransDamperD * FreeJoint1_f6;

  536. 	FreeJoint1_relW = [FreeJoint1_e1, FreeJoint1_e2, FreeJoint1_e3, FreeJoint1_e4, FreeJoint1_e5, FreeJoint1_e6];

  537. 	FreeJoint1\ConnectionPoint1_effort = -FreeJoint1_relW;

  538. 	FreeJoint1\ConnectionPoint2_effort = FreeJoint1_relW * Adjoint (FreeJoint1_relH);

  539. 	markerFree\skewP4to6 = skew (P[4:6]);

  540. 	markerFree\Bk[1:3, 1:3] = skew (P[1:3]);

  541. 	markerFree\Bk[4:6, 1:3] = markerFree\skewP4to6;

  542. 	markerFree\Bk[1:3, 4:6] = markerFree\skewP4to6;

  543. 	TMSum2 = TM2;

  544. 	PDotBodies[1:6] = -[TMSum2 * (adjAdjX2_1 * T2_00);

  545. 				TMSum2 * (adjAdjX2_2 * T2_00);

  546. 				TMSum2 * (adjAdjX2_3 * T2_00);

  547. 				TMSum2 * (adjAdjX2_4 * T2_00);

  548. 				TMSum2 * (adjAdjX2_5 * T2_00);

  549. 				TMSum2 * (adjAdjX2_6 * T2_00)] - markerFree\Bk * v[1:6];

  550. 	grippertopFree\skewP4to6 = skew (P[10:12]);

  551. 	grippertopFree\Bk[1:3, 1:3] = skew (P[7:9]);

  552. 	grippertopFree\Bk[4:6, 1:3] = grippertopFree\skewP4to6;

  553. 	grippertopFree\Bk[1:3, 4:6] = grippertopFree\skewP4to6;

  554. 	TMSum3 = TM3;

  555. 	PDotBodies[7:12] = -[TMSum3 * (adjAdjX3_1 * T3_00);

  556. 				TMSum3 * (adjAdjX3_2 * T3_00);

  557. 				TMSum3 * (adjAdjX3_3 * T3_00);

  558. 				TMSum3 * (adjAdjX3_4 * T3_00);

  559. 				TMSum3 * (adjAdjX3_5 * T3_00);

  560. 				TMSum3 * (adjAdjX3_6 * T3_00)] - grippertopFree\Bk * v[7:12];

  561. 	gripperbaseFree\skewP4to6 = skew (P[16:18]);

  562. 	gripperbaseFree\Bk[1:3, 1:3] = skew (P[13:15]);

  563. 	gripperbaseFree\Bk[4:6, 1:3] = gripperbaseFree\skewP4to6;

  564. 	gripperbaseFree\Bk[1:3, 4:6] = gripperbaseFree\skewP4to6;

  565. 	TMSum4 = TM4;

  566. 	PDotBodies[13:18] = -[TMSum4 * (adjAdjX4_1 * T4_00);

  567. 				TMSum4 * (adjAdjX4_2 * T4_00);

  568. 				TMSum4 * (adjAdjX4_3 * T4_00);

  569. 				TMSum4 * (adjAdjX4_4 * T4_00);

  570. 				TMSum4 * (adjAdjX4_5 * T4_00);

  571. 				TMSum4 * (adjAdjX4_6 * T4_00)] - gripperbaseFree\Bk * v[13:18];

  572. 	PDot = PDotBodies + transpose (wrenchGrav2 * J2 + wrenchGrav3 * J3 + wrenchGrav4 * J4 + transpose (marker2.e) * J2 + transpose (grippertop2.e) * J3 + transpose (gripperbottom.e) * J4 + FreeJoint1\ConnectionPoint1_effort * FreeJoint1\ConnectionPoint1\invAdjointH * J3 + FreeJoint1\ConnectionPoint2_effort * FreeJoint1\ConnectionPoint2\invAdjointH * J4);

  573. 	P = int (PDot) + PDotInitial;

  574. 	v = linsolve (MassMatrix, P, 'cholesky');

  575. 	markerFree\vgen = v[1:6];

  576. 	grippertopFree\vgen = v[7:12];

  577. 	gripperbaseFree\vgen = v[13:18];

  578. implementation_end;

  579.   end;

  580.   connections

  581.   end;

  582.  implementation_end;

  583. ]]>

  584. </Sidops>

  585.  </Model>

  586.  <Experiments>

  587.      <DefaultExperiment><![CDATA[Experiment 1]]>

  588. </DefaultExperiment>

  589.   <Experiment>

  590.     <Name>Experiment 1</Name>

  591.     <CreatedBy></CreatedBy>

  592.     <Info></Info>

  593. <ExpData>

  594.   <VersionNumber>4.8</VersionNumber>

  595.   <ModelProperties>

  596.   </ModelProperties>

  597.   <Variables>

  598.    <Parameters>

  599.    </Parameters>

  600.   </Variables>

  601.   <PlotSpecs>

  602.    <VarNames>

  603.     <VarName>time</VarName>

  604.    </VarNames>

  605.    <Plots>

  606.     <Plot>

  607.      <PlotType>GraphPlot</PlotType>

  608.      <BasePlot>

  609.        <PlotId>1</PlotId>

  610.        <UseWindowsBGColor>false</UseWindowsBGColor>

  611.        <BGColor>16777215</BGColor>

  612.        <PlotIsVisible>true</PlotIsVisible>

  613.      </BasePlot>

  614.      <Grid>

  615.       <DrawGrid>true</DrawGrid>

  616.       <GridColor>15780518</GridColor>

  617.       <GridBorderLineColor>12624260</GridBorderLineColor>

  618.       <GridZeroLineColor>0</GridZeroLineColor>

  619.       <XTicks>10</XTicks>

  620.       <YTicks>10</YTicks>

  621.       <ZTicks>10</ZTicks>

  622.       <Use3DLook>false</Use3DLook>

  623.      </Grid>

  624.      <PlotBGColor>16777215</PlotBGColor>

  625.      <ShowPlotTitle>true</ShowPlotTitle>

  626.      <TitlePosition>1</TitlePosition>

  627.      <PlotTitle>endeffector</PlotTitle>

  628.      <ShowXValues>true</ShowXValues>

  629.      <Fonts>

  630.       <TitleFont>

  631.        <Name>Arial</Name>

  632.        <Height>12</Height>

  633.        <PitchFamily>34</PitchFamily>

  634.        <Weight>400</Weight>

  635.        <Italic>0</Italic>

  636.        <UnderLine>0</UnderLine>

  637.        <StrikeOut>0</StrikeOut>

  638.        <Color>0</Color>

  639.       </TitleFont>

  640.       <LabelFont>

  641.        <Name>Arial</Name>

  642.        <Height>12</Height>

  643.        <PitchFamily>34</PitchFamily>

  644.        <Weight>400</Weight>

  645.        <Italic>0</Italic>

  646.        <UnderLine>0</UnderLine>

  647.        <StrikeOut>0</StrikeOut>

  648.        <Color>0</Color>

  649.       </LabelFont>

  650.       <ValuesFont>

  651.        <Name>Arial</Name>

  652.        <Height>10</Height>

  653.        <PitchFamily>34</PitchFamily>

  654.        <Weight>400</Weight>

  655.        <Italic>0</Italic>

  656.        <UnderLine>0</UnderLine>

  657.        <StrikeOut>0</StrikeOut>

  658.        <Color>0</Color>

  659.       </ValuesFont>

  660.       <LegendFont>

  661.        <Name>Arial</Name>

  662.        <Height>12</Height>

  663.        <PitchFamily>34</PitchFamily>

  664.        <Weight>400</Weight>

  665.        <Italic>0</Italic>

  666.        <UnderLine>0</UnderLine>

  667.        <StrikeOut>0</StrikeOut>

  668.        <Color>0</Color>

  669.       </LegendFont>

  670.      </Fonts>

  671.      <SharedXAxis>true</SharedXAxis>

  672.      <SharedYAxis>true</SharedYAxis>

  673.      <SharedZAxis>false</SharedZAxis>

  674.      <XAxes>

  675.       <Axis>

  676.        <Minimum>0.0</Minimum>

  677.        <Maximum>10.0</Maximum>

  678.        <Linear>true</Linear>

  679.        <Scaling>3</Scaling>

  680.        <Label>time</Label>

  681.       </Axis>

  682.      </XAxes>

  683.      <YAxes>

  684.       <Axis>

  685.        <Minimum>0.0</Minimum>

  686.        <Maximum>10.0</Maximum>

  687.        <Linear>true</Linear>

  688.        <Scaling>2</Scaling>

  689.        <Label></Label>

  690.       </Axis>

  691.      </YAxes>

  692.      <ZAxes>

  693.      </ZAxes>

  694.      <Curves>

  695.       <Curve>

  696.        <LineColor>3355111</LineColor>

  697.        <LineStyle>1</LineStyle>

  698.        <TickColor>3355111</TickColor>

  699.        <TickStyle>0</TickStyle>

  700.        <CurveVisible>true</CurveVisible>

  701.        <PixelThresshold>1</PixelThresshold>

  702.        <LineThickness>1</LineThickness>

  703.        <LineOrder>1</LineOrder>

  704.        <ShowYValues>true</ShowYValues>

  705.        <XCurveData>

  706.         <ShowUnit>true</ShowUnit>

  707.         <VarName>time</VarName>

  708.        </XCurveData>

  709.       </Curve>

  710.      </Curves>

  711.      <Legenda>

  712.       <ShowLegenda>true</ShowLegenda>

  713.       <BorderPenColor>0</BorderPenColor>

  714.       <BackgroundColor>16777215</BackgroundColor>

  715.      </Legenda>

  716.     </Plot>

  717.    </Plots>

  718.    <PlotPanels>

  719.     <PlotPanel>

  720.      <PlotPanelId>1</PlotPanelId>

  721.      <PlotPanelVisible>true</PlotPanelVisible>

  722.      <Name>Window 1</Name>

  723.      <Tiling>0</Tiling>

  724.      <PlotIds>

  725.        <PlotId>1</PlotId>

  726.      </PlotIds>

  727.      <ToggleState>Base</ToggleState>

  728.     </PlotPanel>

  729.    </PlotPanels>

  730.   </PlotSpecs>

  731.   <RunSpecs>

  732.    <SimulatorSettings>

  733.     <StartTime>0.0</StartTime>

  734.     <FinishTime>10.0</FinishTime>

  735.     <AllowPassFinishTime>false</AllowPassFinishTime>

  736.     <Warp>false</Warp>

  737.     <FPGonio>false</FPGonio>

  738.     <UseOutputAfterEach>false</UseOutputAfterEach>

  739.     <OutputAfterEach>0.1</OutputAfterEach>

  740.     <EventEpsilon>1.0e-6</EventEpsilon>

  741.     <AlgebraicTolerance>1.0e-7</AlgebraicTolerance>

  742.     <SteadyStateAnalysis>false</SteadyStateAnalysis>

  743.     <UpdateHoldInstructions>true</UpdateHoldInstructions>

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