Final Project - Designing Mechatronic Systems for Rehabilitation. With the progressively ageing of the population, the proportion of elders is strongly increasing. Linked to this stage of life are the many physical impairments that arise due to an increased frailty caused by disease or simply by the wear of body parts. In the following pages, we will study some of the most important organs and systems associated with balance maintenance. And, when not working properly, they may lead to injury or premature deaths. Sorbonne Université - 5th Year - 1st Semester - Mechatronic Systems for Rehabilitation.

1. Designing Mechatronic Systems For Rehabilitation
[5AH12]
Human Balance - ZMP
PPT Overview
→ Introduction
→ ZMP
→ ZMP, FZMP & CoP
→ References

2. Introduction
→ Proportion of elders is strongly increasing at a global scale;
→ Due to the frailty linked with ageing, problems like falls caused by lack
of balance are becoming more common.
→ In spite of not being a central issue in our societies, falls are
responsible for a greater number of deaths, when comparing to car
accidents.
Global Concern
Human Anatomy
Main systems responsible for human balance are:
Vision Vestibular System Somatosensory System
→ 2 types of receptors in
retina: cones and rods;
→ Access relative distances
to ≠ objects.
→ Vestibular apparatus detects motion,
equilibrium and spatial orientation;
→ Unbalance when contradictory info is
sent to CNS from ≠ sources.
→ Proprioceptive/exteroceptive info
obtained from body receptors…
→ Variations of pressure/stretch are the
triggers.
Fig. 1 – Median age worldwide in 2016. [1]
Fig. 2 – Deaths due to falls per million
persons in 2012. [2]
Fig. 3 – Death rates comparison. [3]
Fig. 4 - Human eye. [4] Fig. 5 – Inner ear. [5] Fig. 6 – Tiptoeing. [6]

3. Zero Moment Point [ZMP]
Dynamic Stability
𝑅 + 𝐹$ + 𝑚& 𝑔⃗ = 0
𝑂𝑃×𝑅 + 𝑂𝐺×𝑚& 𝑔⃗ + 𝑀$ + 𝑀 + 𝑂𝐴×𝐹$ = 0
Equations Static Equilibrium
Forces & Momenta ID
𝑚& 𝑔⃗ - Weight of the foot (in point G – Centre of Mass);
𝐹$ , 𝑀$ - Force & momentum from the upper part of
the body (in point A – ankle joint);
𝑅 → 𝑅 𝑥, 𝑅 𝑦, 𝑅 𝑧 , 𝑀 → (𝑀𝑥, 𝑀𝑦, 𝑀𝑧) – Force &
momentum induced by ground interaction.
𝑀8 = 𝑀9: = −(𝑀$
8
+ 𝑂𝐴×𝐹$
8
<
𝑂𝑃×𝑅
=
+ 𝑂𝐺×𝑚& 𝑔⃗
=
+ 𝑀$
=
+ 𝑂𝐴×𝐹$
=
= 0
Projecting Horizontal Plane
Projecting z-Axis
→ Horizontal components of 𝑅 and 𝑀 are balanced by
friction;
→ 𝑅 𝑥 and 𝑅 𝑦 will cancel the respective components of 𝐹𝐴.
→ 𝑀𝑧 generated by the 2 ground reaction components will
cancel out: vertical 𝑀 𝐴 and the one induced by 𝐹𝐴.
→ In a non-sliding environment, static friction compensates
for 𝑅 𝑥 and 𝑅 𝑦, as well as for 𝑀𝑧.
→ 𝑅 𝑧 will balance all vertical forces applied in the foot.
→ If ankle momentum varies, there will be a change in
position of reaction force and, consequently, momentum
in 𝑥 and 𝑦 directions will be null. If support polygon is
too small, the point of application of force R will move to
the foot edge and the uncompensated horizontal
components of the momentum will induce rotation.
ZMP Definition
Point that results from the
intersection of an axis of
constant vertical momentum with
the plane of the support polygon.
Fig. 7 – Biped robot w/ representation of
forces and momenta. [7]

4. Zero Moment Point [ZMP]
FZMP [Ficititious ZMP]
When ZMP is out of the support polygon, then it is usually called FZMP. As bigger the
distance to the edge of the foot, as significate was the induced unbalance.
Fig. 8 – 3 possible scenarios between ZMP and CoP in a non-rigid foot. [7]
Fig. 9 – Controlled movement using ZMP concept. [8]
CoP [Centre of Pressure]
It is the point where the pressure applied by the ground on the foot can be replaced
by a single force vector. If it balances the other forces applied in the mechanism,
then it is ZMP as well. When there is unbalance, then CoP and ZMP do not coincide.
Once the 1st can only be present in the contact surface, the 2nd vanishes and gives
place to another quantity already addressed – FZMP, out of the support polygon.
Video
Using a dynamic approach instead of static, it turns possible to increase the speed of
movement and reliability, conducting to a more human-like gate.

5. References
[1] List of countries by median age. In: Wikipedia [Internet]. 2017 [cited 2018 Jan 11]. Available from:
https://en.wikipedia.org/w/index.php?title=List_of_countries_by_median_age&oldid=813536623;
[2] Falling (accident). In: Wikipedia [Internet]. 2018 [cited 2018 Jan 11]. Available from:
https://en.wikipedia.org/w/index.php?title=Falling_(accident)&oldid=818999043;
[3] Products - Data Briefs - Number 199 - May 2015 [Internet]. [cited 2018 Jan 11]. Available from:
https://www.cdc.gov/nchs/products/databriefs/db199.htm;
[4] Human eye. In: Wikipedia [Internet]. 2018 [cited 2018 Jan 11]. Available from:
https://en.wikipedia.org/w/index.php?title=Human_eye&oldid=818786738;
[5] Vestibular system. In: Wikipedia [Internet]. 2017 [cited 2018 Jan 11]. Available from:
https://en.wikipedia.org/w/index.php?title=Vestibular_system&oldid=812197324;
[6] The polite killer of any relationship | My Best Relationship [Internet]. [cited 2018 Jan 11]. Available from: https://mybestrelationship.com/the-
polite-killer-of-any-relationship/;
[7] Vukobratović M, Borovac B. Zero-moment point — thirty five years of its life. Int J Humanoid Robot. 2004 Mar 1;01(01):157–73; [MAIN ARTICLE]
[8] HamburgBitBots. ZMP-Walking Demo [Internet]. [cited 2018 Jan 11]. Available from: https://www.youtube.com/watch?v=upABDqQyK9U.