lunes, 2 de marzo de 2015

Dynamical analysis of the sit to stand movement

In order to simplify the analysis, there are some considerations that should be taken before proceeding with the calculations,

1     Initial considerations:


 The human body has been divided in four groups:
o    The first group is formed by the feet, which are considered immobile and serve inertial reference system for the entire Sit-to-stand movement.
o    The second group corresponds to the legs, which rotate on reference of the feet with ankle’s axis.
o    The third group is made up of the thighs, which rotate on reference of the legs with knee’s axis and finally.
o    The fourth group, which, for reasons of simplifying calculations, consider together the trunk, head and upper limbs. This rotates on reference of the third element (thighs) with knee’s axis with hip’s axis.
 The relative parameters: weight, center of gravity, location and radius of gyration, which have been used for this work, are based on anthropomorphic models, obtained from samples of body parts, made by Dempster-Winter (1955, amended in 2009) and Zatsiorsky-Seluyanov, (1996, amended in 2002). See Table 02.

Segment
Center of gravity (%)
Relative Weight (%)
Radius of gyration
Kxx
Radius of gyration
Kyy
Radius of gyration
Kzz
Head and neck
60.4
0.0694
0.362
0.312
0.376
Trunk
49.5
0.4346
0.372
0.191
0.347
Arm
43.6
0.0271
0.285
0.158
0.269
Forearm
43
0.0162
0.276
0.121
0.265
Hand
50.6
0.0061
0.628
0.401
0.513
Thigh
43.3
0.1416
0.329
0.149
0.329
Leg
43.3
0.0433
0.251
0.102
0.246
Foot
42.9
0.0137
0.257
0.124
0.245
TABLE 02: Human body parameters

2     Method of Lagrange – EULER formulation

2.1     Lagrange -equation

$$L=\sum { { E }c_{ i }- } \sum { { E }p_{ i } } $$
$$\sum { { E }c_{ i } } =\frac { 1 }{ 2 } \sum _{ i }^{ n }{ \left[ \overline { v } _{ k }^{ T }{ m }_{ k }{ \overline { v }  }_{ k }+\overline { w } _{ k }^{ T }{ D }_{ k }{ \overline { w }  }_{ k } \right]  } $$
$$\sum { { E }p_{ i } } =-\sum _{ i }^{ n }{ \left[ { m }_{ k }\overline { g } ^{ T }{ \overline { C }  }_{ k } \right]  } $$

Where:

vk:
Translational speed of the k-th element
wk:
Rotational speed of the k-th element
mk:
Mass of the k-th element
Dk:
Inertia tensor of the k-th element regarding X0Y0Z0 and moved to its center of mass..
Ck:
Center of mass of the k-th element
g:
Gravity

3     Method of Newton – EULER formulation

o    The θ1, θ2, θ3, angles were taken on reference of the horizontal axis.
o    Each element is taken as a rigid body.
o    Motion of various part of the body occur in a vector plane so that rotations of the body may be disregarded.
o    Various joint of the body may be expressed as a series of links
o    Each joint has a single axis
o    The center of gravity for each body segment is located along the line extending from one joint to the other.
o    The upper body, including the arms, may be expressed as a single, uniform volume.
o    W1, f1, W2, f2, f0 are defined as follows, according to the report by Matsui: W1, 56% of body weight; f1, 45% of sitting height; W2, 10% of body weight; f2, 58% of femur length; f0, actual measured distance from the outer knee joint to the greater trochanter of the femur.


Comparison between the results of calculation of torque by the Lagrange-Euler equation and the Newton-Euler formulation


4     Conclusions

  • Motion capture is an excellent tool for estimating the direct and inverse kinematics of our system; however, this procedure should be standardized, by parameterizing measures and environmental conditions where it is recorded. Once the recording data is made, it should be consider the ankle as a fixed point throughout the sitto-stand process, allowing this, a better data record.
  • The Lagrange equation and Denavit-Hartemberg representation let us parameterize the kinematic analysis (position, velocity and acceleration) and dynamic (Forces and Toques) versus time, achieving these, the calculus of maximum torques and forces on each element of our model, by noticing that we can consider that we need 1N-m for each kilogram of user’s mass to get manage the sit-to-stand movement. However, it is necessary to apply an additional safety factor when selecting the actuator motor to be used in our exoskeleton.
  • Newton-Euler formulation and Lagrange-Euler show similar results and graphics, corroborating thus the dynamic and kinematic analysis are correct.

Artículo expuesto en el 9th international Convention on Rehabilitation Engineering and Assistive Technology (i-CREATe 2015) del Enabling Technology Festival en Singapur - powered by IEEE


No hay comentarios: