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CDraw40CorelDRAW!/ 0DTimes New Romanhbb`0b0DArialNew Romanhbb`0b0" DSymbolew Romanhbb`0b0 a .  @n?" dd@  @@`` ZRHd     )!,2$kk%@'biUqZc $0e0e     A@  Ao ))     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||S"@ {uʚ;2Nʚ;g4`d`d`0bppp@ <4!d!dW0bTb<4ddddW0bTb <4BdBd b׽0bb?V+ BBiomechanics Lab, Univ. of OttawaO =Measurement of Internal WorkwD. Gordon E. Robertson, Ph.D. Biomechanics Laboratory, School of Human Kinetics, University of Ottawa, Ottawa, CANADARx >Mechanical EnergyFour forms Gravitational potential m g y Elastic potential k s2 Translational kinetic m v2 Rotational kinetic I w2 Total mechanical energy is sum of all four Elastic potential energy is usually omitted because it cannot be measured accurately< q = Total Body Mechanical EnergySum of all segmental total mechanical energies (Es) Segmental total energy Es = ms g ys + ms vs2 + Is ws2 Total body energy Etotal = S Es K$1                              ,T*  External WorkMechanical work = change in mechanical energy Wext = S (D Etotal) or simplified Wext = Etotal(tn)  Etotal(t0).-  $$$$$$$  $$$$$$$$$$$$t. Zero-work ParadoxIf a body moves at constant velocity along a horizontal path no  external mechanical work is done! Mechanical cost of moving body parts cancel out if motion is cyclic. Problem exists with all locomotor tasks but if body speeds up or rises, some external work is done, however, additional costs of  cycling the body parts are not included.FUP)2Work Allowing No Transforms or Transfers of EnergyWork done that prevents changes of forms of energy, i.e., from potential to kinetic, etc. Wn = S S | D ms g ys | + | D ms vs2 | + | D Is ws2| First summation is over all time intervals Second summation is over all segments Norman et al. (1976)ZEf[                          f>['Work Allowing within Segment TransformsWork done that permits changes of forms of energy within a segment (kinetic to potential and vice versa) but no transfers from segment to segment Ww = S S | D Es | First summation is over all time intervals Second summation is over all segments Winter (1979)_2% +,,,,,,,,,_o ;Energy Conservation by Transforming Energy within a Segmentsimple pendulum   Internal Work#Internal work measures the mechanical costs of moving the limbs during a cyclic motion. The equation permits transfers of energy from segment to segment and from one form to another. Wint = S | D Etotal | - Wext Absolute values prevent decreases in mechanical energy from canceling increasesP ((((((((((P> Q ;Energy Conservation by Transferring Energy between Segmentscompound pendulum (Energy Saved by Transfers and TransformsEnergy saved by permitting transfers of energy from segment to segment Etransfers = Wnt - Wint Energy saved by permitting transforms of energy from one form to another (potential ot kinetic) Etransforms = Wn - Wnt G`G      `      G U  Segment Energies during Walking/  ` ̙33` 3` 3333f` 999MMM` f` f3` 3>?" dZ@$|? " dZ@  @" `  n?" dd@   @@``PR    @ ` ` p>  >   ^(     `*gֳgֳ ?"`k  @*    `.gֳgֳ ?"`   B*    `3gֳgֳ ?"`  B*   ZD3gֳgֳ ?"kP  ? 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EntrydO)PUPictures,'Current UserbSummaryInformation(8U!/ 0DTimes New RomanDrbb`0b0DArialNew RomanDrbb`0b0" DSymbolew RomanDrbb`0b0 a .  @n?" dd@  @@`` Pt    )!/X2$kk%@'biUqZb$=J֗-uvC XZc $0e0e     A@  Ao ))     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||S"@ {uʚ;2Nʚ;g4`d`d`0bppp@ <4!d!dW0b0rb<4ddddW0b0rb <4BdBd b׽0bb?V+ BBiomechanics Lab, Univ. of OttawaO =&7Measurement of Internal Work using Absolute Work MethodwD. Gordon E. Robertson, Ph.D. Biomechanics Laboratory, School of Human Kinetics, University of Ottawa, Ottawa, CANADARx >Mechanical EnergyFour forms Gravitational potential m g y Elastic potential k s2 Translational kinetic m v2 Rotational kinetic I w2 Total mechanical energy is sum of all four Elastic potential energy is usually omitted because it cannot be measured accurately< q = Total Body Mechanical EnergySum of all segmental total mechanical energies (Es) Segmental total energy Es = ms g ys + ms vs2 + Is ws2 Total body energy Etotal = S Es K$1                              ,T*  External WorkMechanical work = change in mechanical energy Wext = S (D Etotal) or simplified Wext = Etotal(tn)  Etotal(t0).-  $$$$$$$  $$$$$$$$$$$$t. Zero-work ParadoxIf a body moves at constant velocity along a horizontal path no  external mechanical work is done! Mechanical cost of moving body parts cancel out if motion is cyclic. Problem exists with all locomotor tasks but if body speeds up or rises, some external work is done, however, additional costs of  cycling the body parts are not included.FUP)2Work Allowing No Transforms or Transfers of EnergyWork done that prevents changes of forms of energy, i.e., from potential to kinetic, etc. Wn = S S | D ms g ys | + | D ms vs2 | + | D Is ws2| First summation is over all time intervals Second summation is over all segments Norman et al. (1976)ZDfZ                          f>Z'Work Allowing within Segment TransformsWork done that permits changes of forms of energy within a segment (kinetic to potential and vice versa) but no transfers from segment to segment Ww = S S | D Es | First summation is over all time intervals Second summation is over all segments Winter (1979)_2% +,,,,,,,,,_o ;Energy Conservation by Transforming Energy within a Segmentsimple pendulum   Internal Work#Internal work measures the mechanical costs of moving the limbs during a cyclic motion. The equation permits transfers of energy from segment to segment and from one form to another. 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OBf @7n07$&uFs4/8b'fyrzL{A#(_b ad:[C\7jĭaElpǞA'ieD6w7DG72rgܟ;̺}9xx˾#^/ V;XDyA]bzĆHf}xF_Lԗ`IJ9ԙFw&y?# "C Ͱ5'{ߦjFSzB̡3Aı>5 jsJo;2&={CHn@f;cjcHdFXR+fі!ۢOiPFwh"σ˘z`n衫×zoն{1DTP 4cW<'ND~"gta\c:IL=LI5 \6TAx#a_J_EvuE<IH{gٜ>^[GL[iM'氠r9 /NE<0vLpwս4>FJRnZ Jv=;ތ ݫ}4OgάMfKmgl>N}938][MmiB,nvS{oXpf#jP:xzoWӶx犨w= M#&.eCDQI&xGo?ì߁՟՟7< ޛ_?Ό6XIENDB` / 0DTimes New RomanDDkbb`0b0DArialNew RomanDDkbb`0b0" DSymbolew RomanDDkbb`0b0 a .  @n?" dd@  @@`` ~Pq     )!/X2$kk%@'biUqZib$=J֗-uvC XZic $0e0e     A@  Ao ))     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||S"@ {uʚ;2Nʚ;g4`d`d`0bppp@ <4!d!dW0b0Ekb<4ddddW0b0Ekb <4BdBd b׽0bb?V+ BBiomechanics Lab, Univ. of OttawaO =Measurement of Internal WorkwD. Gordon E. Robertson, Ph.D. Biomechanics Laboratory, School of Human Kinetics, University of Ottawa, Ottawa, CANADARx >Mechanical EnergyFour forms Gravitational potential m g y Elastic potential k s2 Translational kinetic m v2 Rotational kinetic I w2 Total mechanical energy is sum of all four Elastic potential energy is usually omitted because it cannot be measured accurately< q = Total Body Mechanical EnergySum of all segmental total mechanical energies (Es) Segmental total energy Es = ms g ys + ms vs2 + Is ws2 Total body energy Etotal = S Es K$1                              ,T*  External WorkMechanical work = change in mechanical energy Wext = S (D Etotal) or simplified Wext = Etotal(tn)  Etotal(t0).-  $$$$$$$  $$$$$$$$$$$$t. Zero-work ParadoxIf a body moves at constant velocity along a horizontal path no  external mechanical work is done! Mechanical cost of moving body parts cancel out if motion is cyclic. Problem exists with all locomotor tasks but if body speeds up or rises, some external work is done, however, additional costs of  cycling the body parts are not included.FUP)2Work Allowing No Transforms or Transfers of EnergyWork done that prevents changes of forms of energy, i.e., from potential to kinetic, etc. Wn = S S | D ms g ys | + | D ms vs2 | + | D Is ws2| First summation is over all time intervals Second summation is over all segments Norman et al. (1976)ZEf[                          f>['Work Allowing within Segment TransformsWork done that permits changes of forms of energy within a segment (kinetic to potential and vice versa) but no transfers from segment to segment Ww = S S | D Es | First summation is over all time intervals Second summation is over all segments Winter (1979)_2% +,,,,,,,,,_o ;Energy Conservation by Transforming Energy within a Segmentsimple pendulum   Internal Work#Internal work measures the mechanical costs of moving the limbs during a cyclic motion. The equation permits transfers of energy from segment to segment and from one form to another. Wint = S | D Etotal | - Wext Absolute values prevent decreases in mechanical energy from canceling increasesP ((((((((((P> Q ;Energy Conservation by Transferring Energy between Segmentscompound pendulum (Energy Saved by Transfers and TransformsEnergy saved by permitting transfers of energy from segment to segment Etransfers = Wnt - Wint Energy saved by permitting transforms of energy from one form to another (potential ot kinetic) Etransforms = Wn - Wnt G`G      `      G U  Segment Energies during Walking/   v n D (  Dx D c $P_0P  k  D C fAND:\Docs\DGER\Book2\GRAPHICS\ENERGY.GIF sdz  D `L ,$D 0B D  gֳgֳD)))? pq  D c L,[gֳgֳ ԔԔ? Pno conservation in the leg( 2hz @ , D @ ,,$D 0B  D  gֳgֳD)))? 0   D c ([gֳgֳ ԔԔ?@ @, Tsome conservation in the thigh( 2hz `  D ` ,$D 0B DB  gֳgֳD)))?`P D c [gֳgֳ ԔԔ?@  Tsome conservation in the trunk( 2`l  | D |,$D 0 D c [gֳgֳ ԔԔ? | `*some transfer between left and right sides+( 2+B DB  gֳgֳD)))?`H D 0޽h ? inCa1r*O)s O~t((   |rCorelDRAW!  CDraw40CorelDRAW._@UD. Gordon E. RobertsonD. Gordon E. Robertsonson, Ph.D. Titles ՜.+,0     [On-screen ShowMcLean-RobertsondUO  Times New RomanArialSymbolBIOMECH CorelDRAW!5Measurement of Internal Work by Absolute Work MethodMechanical EnergyTotal Body Mechanical EnergyExternal WorkZero-work Paradox3Work Allowing No Transforms or Transfers of Energy(Work Allowing within Segment Transforms<Energy Conservation by Transforming Energy within a SegmentInternal Work<Energy Conservation by Transferring Energy between Segments)Energy Saved by Transfers and Transforms Segment Energies during WalkingEquation Summary  Fonts UsedDesign TemplateEmbedded OLE Servers Slidel energy from canceling increasesP ((((((((((P> Q ;Energy Conservation by Transferring Energy between Segmentscompound pendulum (Energy Saved by Transfers and TransformsEnergy saved by permitting transfers of energy from segment to segment Etransfers = Wnt - Wint Energy saved by permitting transforms of energy from one form to another (potential ot kinetic) Etransforms = Wn - Wnt G`G      `      G U  Segment Energies during Walking Equation SummaryvWn = S S | D PEs | + | D KEs | + | D PEs | Ww = S S | D Es | Wwb = S | D S Es | Wext = S S D Etotal Wint = Wwb - Wext w$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  /*  0 R(      BA ??vE Z $ $00hhh333333ffffffffffffffffff333333   `ζgֳgֳ ?P     # lζgֳgֳ ?V   H  0޽h ? inCa1  40(  4x 4 c $rP  r x 4 c $Lrk r H 4 0޽h ? inCa1;   @ k(  @x @ c $9P   x @ c $H:k   @  `0]o))?  @ Z   @  `))?``  B @ ZD>))?j8   @ B  @B ZD>))?  0 B  @B  `D>))?0   @  BCDEFo))?LHHH@  P  @ ZXFro))?  @ Z   @ Z))? ` |B @ TD>))?   @ s gֳgֳ    BCDELF$ @  Ԕ ԔԔ     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||)\eX v3  yQ{K@      )  @@ s gֳgֳ    BCDELF$ @  Ԕ ԔԔ     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||)\eX v3  yQ{K@      @ Oz  0  @  0 ,$D 0B @  gֳgֳD)))?Pp 0p  @ S ~`]rgֳgֳ ԔԔ?   Gproximal segment ( 2Jz   ` @   ,$D 0B @  gֳgֳD)))? ` `  @ S ~argֳgֳ ԔԔ?p ` B total energy ( 2 Lz  0  @ P 0V,$D 0B @  gֳgֳD)))?Pp 0p  @ S ~ergֳgֳ ԔԔ?   Ddistal segment( 2B @ ZD>))? B @  `D>))? 0P   @  BC8DEFo))?3+*8sI7@  m  H @ 0޽h ? inCa1  L0(  Lx L c $-rP  r x L c $lr r H L 0޽h ? inCa1r(3ħ1 )t2(    | CorelDRAW!  CDraw40CorelDRAW!/ 0DTimes New RomanTT|vܖx: 0ܖDArialNew RomanTT|vܖx: 0ܖ" DSymbolew RomanTT|vܖx: 0ܖ A .  @n?" dd@  @@`` !t)!/X2$kk%@'biUqZb$=J֗-uvC XZc $0e0e     A@  Ao ))     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||S"@ ʚ;ʚ;g4kdkd0x: 0ppp@ <4!d!d  0TXv<4dddd  0TXv <4BdBd  0T80___PPT10 pp?V+ BBiomechanics Lab, Univ. of OttawaO =( 4Measurement of Internal Work by Absolute Work Method~D. Gordon E. Robertson, PhD, FSCB Biomechanics Laboratory, School of Human Kinetics, University of Ottawa, Ottawa, CANADAJ">Mechanical EnergyFour forms Gravitational potential (Egp) m g y Elastic potential (Eep) k Ds2 Translational kinetic (Etk) m v2 Rotational kinetic (Erk) I w2 Total mechanical energy is sum of all four Elastic potential energy is usually omitted because it cannot be measured accurately\      =P$"Total Body Mechanical EnergySum of all segmental total mechanical energies (Es) Segmental total energy Es = ms g ys + ms vs2 + Is ws2 Total body energy (Etotal, sum over all segments) Etotal = S Es KP$P2PPP0                                    >U+  External Work"External work = change (D) in total body mechanical energy Wexternal = S (D Etotal) or simplified Wexternal = Etotal (tfinal)  Etotal (tinitial);0  !  $$$$$$$  $$$$$$$$$$$$$$$$$$$;  Zero-work ParadoxIf a body moves at constant velocity along a horizontal path no  external mechanical work is done (work = 0)! Mechanical cost of moving body parts cancel out if motion is cyclic. Problem exists with all locomotor tasks but if body speeds up or rises (e.g., treadmill), some external work is done BUT additional costs of  cycling the body parts are not included.FlP)2Work Allowing No Transforms or Transfers of Energy(Work done that prevents both transfers and transforms of energy, i.e., from potential to kinetic and from segment to segment. Wn = S S | D ms g ys | + | D ms vs2 | + | D Is ws2| First summation is over all time intervals Second summation is over all segments Norman et al. (1976)PfP                            X,'Work Allowing within Segment TransformsWork done that permits changes of forms of energy within a segment (kinetic to potential and vice versa) but no transfers from segment to segment. Ww = S S | D Es | First summation is over all time intervals Second summation is over all segments Winter (1979)_2% ,,,,,,,,,,_o;Energy Conservation by Transforming Energy within a Segmentsimple pendulum  Internal WorkInternal work measures the mechanical costs of moving the limbs during a cyclic motion. The equation permits transfers of energy from segment to segment and transforms from one form (Egp, Etk) to another. Winternal = S | D Etotal | " Wexternal Absolute values prevent decreases in mechanical energy from cancelling increases4'Q   (((((((((( (Qb   R;Energy Conservation by Transferring Energy between Segmentscompound pendulum  (Energy Saved by Transfers and TransformsEnergy saved by permitting transfers of energy from segment to segment Etransfers = Ww " Winternal Energy saved by permitting transforms of energy from one form to another (potential ot kinetic) Etransforms = Wn " Ww\G`G        `        G  V !Segment Energies during Walking Equation SummarydWn = S S | D ms g ys | + | D ms vs2 | + | D Is ws2| Ww = S S | D Es | Wtotal = S | D S Es | = Wwb Wexternal = S S D Etotal = Efinal " Einitial Winternal = Wtotal " Wexternal   $                         $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$    /"*  0L0  PR(  P P BA  ??2# $  $ 0X 0hhh333333ffffffffffffffffff333333 P  ` gֳgֳ ?P     P # ld gֳgֳ ?V    H P 0޽h ? inCa1  0 @X0(  Xx X c $/ kP  /  x X c $/  /  H X 0޽h ? inCa1  0 P\0(  \x \ c $/ P  /  x \ c $X/  /  H \ 0޽h ? inCa1  0 ``<(  `~ ` s *,&/ kP  /  ~ ` s *M/ d /  H ` 0޽h ? ̙33  0 pd0(  dx d c $W/ kP  /  x d c $t/  /  H d 0޽h ? inCa1  0 h0(  hx h c $/ P  /  x h c $P/ k /  H h 0޽h ? inCa1  0 l0(  lx l c $̷/ kP  /  x l c $/ k /  H l 0޽h ? inCa1(  0  p(  px p c $l/ P  /  x p c $/ k /  z P ` p ` ,$D 0 p Z`/ o))?P @` . Z  p Z))? B p TD>))?P `2 p S ~ @>))?P p  p  fH0 ))?Q   @pendulum  Z  B  pB TD>))?`@ B  p ZD>))?pP 2  p S ~ @))?P p  p  BCDEFo))?LHHH@  P `  p Z0 o))?  . Z  p Z))? ` |B p TD>))?   p s gֳgֳ    BCDELF$ @  Ԕ ԔԔ     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||)\eX v3  yQ{K@      )  p@ s gֳgֳ    BCDELF$ @  Ԕ ԔԔ     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||)\eX v3  yQ{K@      @ Nz  0  p  0 ,$D 0B p  gֳgֳD)))?Pp 0p  p S ~0 gֳgֳ ԔԔ?   Fpotential energy( 2Jz   ` p  @ ,$D  0B p  gֳgֳD)))? ` `  p S ~'0 gֳgֳ ԔԔ?p ` B total energy ( 2 Lz  0  p P 0V,$D 0B p  gֳgֳD)))?Pp 0p  p S ~10 gֳgֳ ԔԔ?   Dkinetic energy( 2H p 0޽h ? inCa1___PPT10+ۗ+4Dh' = @B D#' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*pDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*pDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*p+  0 t<(  t~ t s *A0 kP  0  ~ t s *F0 pp 0  H t 0޽h ? ̙33'  0 x+(  xx x c $N0 P  0  x x c $4Z0 k 0   x Ztr0 o))?  . Z  x Z))?``  |B x TD>))?lF   x  B xB TD>))?  0 B  xB ZD>))?0   x  BCDEFo))?LHHH@  P   x Z}0 o))?  . 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B x ZD>))? 0P  x  BC8DEFo))?3+*8sI7@  m  H x 0޽h ? inCa1___PPT10+rODh' = @B D#' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*xD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*xDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*xD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*xDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*xD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*x+  0 |0(  |x | c $h0 P  0  x | c $<0 k 0  H | 0޽h ? inCa1      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrs  0    (  ~  s *40 0P  0  N  C &AENERGY s`z   `2 ,$D 0B   gֳgֳD)))? pq  S ~h0 gֳgֳ ԔԔ? 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