Human Motion. Session Speaker Dr. M. D. Deshpande. AML2506 Biomechanics and Flow Simulation PEMP-AML2506

Transcription

1 AML2506 Biomechanics and Flow Simulation Day 02A Kinematic Concepts for Analyzing Human Motion Session Speaker Dr. M. D. Deshpande 1

2 Session Objectives At the end of this session the delegate would have understood Mechanical-Kinematics Concepts Reference positions, planes, and axes associated with the human body Human movement and its analysis 2

3 Session Topics 1. Review of Mechanical-Kinematics Concept 2. Description of the reference positions, planes, and axes associated with the human body 3. Definition and use of directional terms and joint movement terminology 4. A plan to conduct an effective qualitative human movement analysis 5. Identification and description of the uses of available instrumentation for measuring kinematic quantities 3

4 Kinematics of a Particle A particle is a body that is assumed to have mass but negligible physical dimensions. Whenever the dimensions of a body are irrelevant to the problem then the use of particle mechanics may be expected to provide accurate results. Typical applications would be the analysis of the motion of a spacecraft orbiting the earth Rigid-body mechanics which is an approach that needs to be adopted when the dimensions of the body cannot be neglected 4

5 Linear Motion of a Particle under Variable Acceleration 5

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7 Two-Dimensional Motion of a Particle 7

8 Tangential and Normal Coordinates Velocity- Curvilinear Motion It is often convenient to describe curvilinear motion using path variables, i.e., measurements made along the tangent t and normal n to the path. The frame can be pictured as a right-angled bracket moving along with the particle. The t arm always points in the direction of travel, while the n arm points towards the centre of curvature. Unit vectors e t and e n are shown in the Figure. The velocity vector is tangential to path 8

9 Acceleration- Curvilinear Motion 9

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11 Circular Motion 11

12 Polar Coordinates The third option is to locate the particle by the radial distance r and angular position with respect to a chosen fixed direction. We choose unit vectors e r and e as shown Velocity Acceleration 12

13 Kinematics of a Rigid Body Rigid bodies are different from particles: rigid bodies are extended in space, and the connection between different parts of a rigid body are permanent and unchanged throughout their motion. When we try to imagine i the position i of a rigid id body, we may first think of an arbitrary point, a marker (let s call it A), on that body. The position and motion of this chosen point can be described in exactly the same way we used for particles, e.g. using rectangular or polar coordinates. 13

14 Kinematics of a Rigid Body However, the description is insufficient to describe the motion of the rigid body, since the body as a whole may rotate around point A. In order to fix the position of the body we must specify a direction from point A to another arbitrarily chosen point on the body, say B. Once the position of A is fixed, and the direction from A to B is given as well, position of the rigid body is fully specified. e.g. a rigid rod connecting two points A and B is a rigid body. 14

15 Kinematics of a Rigid Body A rigid body is in plane motion if all point of the body move parallel to one plane, which is called the plane of motion. We can classify the kinds of plane motion into: (a) translation (rectilinear) (b) translation (curvilinear) (c) rotation (around fixed axis) (d) general plane motion In translation every line in the body remains parallel to its original position, and no rotation is allowed. The trajectory of motion is the line traced by a point in the body. Translation is rectilinear if this line is straight, and curvilinear otherwise. 15

16 Kinematics of a Rigid Body Rotation about a fixed axis is the angular motion about this axis, when all points on the body follow concentric circular paths. It is important to picture and understand that all lines on the solid body, even those that do not pass through the centre, rotate through the same angle in the same time General plane motion of a rigid body is a combination of translation and rotation. The concept of relative motion comes into picture in order to describe this case. 16

17 Rigid Body Rotation All lines on a rigid body have the same angular displacement, the same angular velocity and the same angular acceleration. 17

18 Relative Motion Let A and B be two points on the rigid body. We start with the following vector relation: R a = R b + R a/b Here Ra and Rb represent absolute position vectors of A and B with respect to some fixed axes, and Ra/b stands for the relative position vector of A with respect to B By differentiating the above equation with respect to time, we obtain the basis of the relative motion analysis, known as the relative velocity equation: V a = V b + V a/b To determine the velocity of A with respect to the fixed axes (the absolute velocity V a ) we represent it as the sum of the absolute velocity of point B, V b, and the relative velocity of point A with respect to point B, V a/b 18

19 When the solid body is rotating around a fixed axis with angular velocity ω, all vectors on that solid body also rotate with the same angular velocity. 19

20 Instantaneous Centre of Rotation The point of reference (about which the references have been made in the previous discussion) is not always fixed. The reference point will be moving along with the body and the coordinate system. The reference point can be taken as centre at a given instant, that is why the centre is known as Instantaneous Centre. 20

21 Kinematic Constraints Two or more rigid bodies in space are collectively called a rigid body system. The motion of independent rigid bodies can be hindered with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid bd body system. The term kinematic pairs actually refers to kinematic constraints between rigid bodies. The kinematic pairs are divided into lower pairs and higher pairs, depending on how the two bodies are in contact. Surface-contact contact pairs are called lower pairs. There are two subcategories of lower pairs -- revolute pairs and prismatic pairs. Point-, line-, or curve-contact pairs are called higher pairs. 21

22 Kinematic Constraints There are two kinds of lower pairs in planar mechanisms: revolute pairs and prismatic pairs. A rigid body in a plane has only three independent motions -- two translational and one rotary -- so introducing either a revolute pair or a prismatic pair between two rigid bodies removes two degrees of freedom. A planar revolute A planar prismatic pair (R-pair) pair (P-pair) 22

23 Kinematic Constraints There are six kinds of lower pairs under the category of spatial mechanisms. The types are: spherical pair, plane pair, cylindrical i lpair, revolute pair, prismatic pair, and screw pair. A spherical pair keeps two spherical centres together. Two rigid bodies connected by this constraint will be able to rotate relatively around x, y and z axes, but there will be no relative translation along any of these axes. Therefore, a spherical pair removes three degrees of freedom in spatial mechanism. DOF = 3. 23

24 Kinematic Constraints A plane pair keeps the surfaces of two rigid bodies together. To visualize this, imagine a book lying on a table where is can move in any direction except off the table. Two rigid bodies connected by this kind of pair will have two independent translational motions in the plane, and a rotary motion around the axis that is perpendicular to the plane. Therefore, a plane pair removes three degrees of freedom in spatial mechanism. In our example, the book would not be able to rise off the table or to rotate into the table. DOF = 3. 24

25 Kinematic Constraints A cylindrical pair keeps two axes of two rigid bodies aligned. Two rigid bodies that are part of this kind of system will have an independent d translational motion along the axis and a relative rotary motion around the axis. Therefore, a cylindrical pair removes four degrees of freedom from spatial mechanism. DOF = 2. Compare with a spatial A3D 3-D cylindrical i lpair (C-pair) i) revolute pair (R-pair). Next figure 25

26 Kinematic Constraints ARevolute pair keeps the axes of two rigid bodies together. Two rigid bodies constrained by a revolute pair have an independent rotary motion around their common axis. Therefore, a revolute pair removes five degrees of ffreedom in spatial mechanism. DOF = 1 A planar revolute A spatial revolute pair (R-pair) pair (R-pair) 26

27 Kinematic Constraints A prismatic pair keeps two axes of two rigid bodies aligned and allows no relative rotation. Two rigid bodies constrained by this kind of constraint will be able to have an independent translational motion along the axis. Therefore, a prismatic pair removes five degrees of freedom in spatial mechanism. DOF = 1. 27

28 Kinematic Constraints A screw pair keeps two axes of two rigid bodies aligned and allows a relative screw motion. Two rigid bodies constrained by a screw pair of motion which is a composition of a translational motion along the axis and a corresponding rotary motion around the axis. Therefore, a screw pair removes five degrees of freedom in spatial mechanism. DOF = 1. 28

29 Gruebler's Equation F = total degrees of freedom in the mechanism n = number of links (including the frame) l = number of lower pairs (one degree of freedom) h = number of fhigher h pairs (two degrees of freedom) This equation is known as Gruebler's Equation 29

30 Gruebler's Equation Type of kinematic pairs (constraints) n Number of links l Number of lower pairs (Surface s) h Number of higher pairs (Points & Lines) F Degrees of freedom (= Translation + Rotation Comments on constraints 1 2-D Free motion (= 2 + 1) n =2 (fixed, Bar) 2 2-D Revolute pair (= 0+ 1) 3 2-D prismatic pair (= 1 + 0) 4 3-D Free motion (= 3 + 3) n =3 (fixed, Bar, Bar in transverse direction) 5 3-D spherical pair ( (= 0+3) Spherical surface, Sphere centre 6 3-D plane pair (= 2 + 1) Planar surface, Line stops rotation 7 3-D cylindrical pair (= 1 + 1) Cylindrical surface allows Translation & Rotation 8 3-D revolute pair (= 0 + 1) Translation is blocked n = D prismatic pair (= 1 + 0) 10 3-D screw pair 3 1( (= 0 + 1) 2 1 or (= 1 + 0) Two planar surfaces l = 2 block rotation Translation & Rotation are coupled 30

31 Kinematic Analysis Ideas discussed in the context of kinematics of particles and rigid bodies will now be used in the analysis of human linkages The objective of kinematic analysis of a mechanism is to determine the linear and angular velocities of the various components of the mechanism when some part of it is subjected to a known linear or angular velocity. Graphical, Analytical and Computer Based Methods are followed for Kinematic Analysis. Here we use LifeMod and ADAMS software packages to do the analysis 31

32 Example-Kinematic Analysis Analytical Approach Find the velocity of C and the angular velocity of link BC in the crankslider mechanism at the instant shown below. The crank AB is rotating anti-clockwise with angular velocity ω = d /dt = 500 rad/s (approx rpm). 32

33 Using the analytical approach, we first write down equations defining the geometry of the mechanism: Next, we need to differentiate the expressions for z and cos. The derivative of the expression for z gives: 33

34 We are now able to calculate the velocity of point C by inserting the appropriate values of r,, d /dt and l into the above expression (noting that d /dt is simply the angular velocity of link AB and therefore equal to 500 rad/s). In this particular case this leads to the solution The angular velocity of link BC is given by d /dt. To evaluate this expression we differentiate the expression for sin (above) to give: 34

35 If specific values of r,,, d /dt and l are substituted into the above expression then this gives a value for the angular velocity of link BC of 189 rad/s. In addition to computing the values of linear and angular velocity for the particular position of the mechanism shown in the example, the results of the analysis can alsobe used to determine the kinematics of the mechanism for all values of. 35

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38 Example-Kinematic Analysis Graphical lapproach 38

39 Example-Kinematic Analysis Solution Using ADAMS 39

40 Anatomical Reference Position Erect standing position with all body parts facing forward considered the starting point for all body segment movements 40

41 Directional Terms superior: closer to the head inferior: farther away from the head anterior: toward the front of the body posterior: toward the back of the body medial: toward the midline of the body lateral: away form the midline of the body proximal: closer to the trunk distal: away from the trunk superficial: toward the surface of the body deep: inside the body away from the surface 41

42 Anatomical Reference Planes Longitudinal axis Anteroposterior axis Medio-lateral axis Frontal plane 42 M.S. Ramaiah School of Advanced Studies - Bangalore 02A

43 Anatomical Reference Planes Cardinal Planes: Three imaginary perpendicular reference planes that divide the body in hlaf by mass Sagittal plane Plane in which forward and backward movements of the body and body segments occur. It is also known as anteroposterior (AP) plane, divides the body vertically into left and right halves of equal mass Frontal plane plane in which lateral movements of the body and body segments occur. It is also known as coronal plane, divides the body vertically into front and back halves of equal mass Transverse plane Plane in which horizontal body and body segments movement occur when the body is an erect standing position. It is also known as horizontal plane, divides the body into top and bottom halves of equal mass For an individual standing in anatomical reference position, the three cardinal planes all intersect at a single point known as the body s centre of mass or centre of gravity Although most human movements are not strictly planar, the cardinal planes provide a useful way to describe movements that are primarily planar 43

44 Sagittal plane movements-example 44

45 Anatomical Reference Axes Mediolateral axis - around which rotations in the sagittal plane occur. It is also known as the frontal-horizontal axis, is perpendicular to the sagittal plane Anteroposterior axis - around which rotations in the sagittal plane occur. It is also known as sagittal horizontal axis and perpendicular to frontal plane. Longitudinal axis - around which rotational movements occur. It is also known as vertical axis. 45

46 Joint Movement All body segments are considered to be at zero degrees at anatomical reference position. Rotation of a body segment away from anatomical position is named according to the direction of motion and measured as the angle between the body segment ss position and anatomical position 46

47 Sagittal Plane Movements Flexion: Extension: Hyperextension: Dorsiflexion: Plantar flexion: Flexion Extension Hyperextension Flexion Extension Hyperextension Dorsiflexion Plantar flexion 47

48 Frontal Plane Movements Abduction & Adduction Lateral flexion Elevation & Depression Inversion &Eversion Radial & Ulnar deviation Radial deviation Ulnar deviation Abduction Adduction Lateral flexion Elevation Depression Eversion Inversion 48

49 Movements in Horizontal Plane Left & Right rotation Medial & Lateral rotation Supination & Pronation Horizontal abduction & adduction Horizontal adduction Medial Lateral rotation ti rotation Pronation Supination Horizontal abduction 49

50 Spatial Reference Systems Useful for standardizing descriptions of human motion Most commonly used is the Cartesian coordinate system Human body joint centers are labeled with numerical x and y coordinates Y (x,y) = (3,7) (0,0) 50 X

51 Qualitative Human Movement Analysis Planning for human movement analysis Performer attire Lighting conditions Background Use of video 51

52 Qualitative Analysis: Conducting Movement Analysis Identify Question/Problem Refine Question Communicate with Performer Make Decisions End Analysis Collect Observations Interpret Observations Viewing Angle Viewing Distance Performer Attire Environmental Modifications Use of Video Visual Auditory From Performer From Other Analysts 52

53 Tools for Measuring Kinematic Quantities Videocamera Electrogoniometer: is a device that can be interfaced to a recorder to provide a graphical record of the angle present at a joint Lights, photocell and Timer are used to measure movement e velocity 53

54 Demos Dynamic Human CD - Available in Windows (ISBN ) Further Demos Ariel Dynamics Worldwide Motion Analysis Corporation SIMI Reality Motion Systems i 54

55 Laboratory Refer laboratory exercises 55

56 Review In this session the delegates are taught: Kinematics of a particle Curvilinear motion Kinematics of a rigid body Kinematic constraints Reference planes and axes associated with the human body Qualitative human movement analysis Identification and description of the uses of instrumentation for measuring kinematic quantities 56

57 Thank you 57