 In biomechanics research, what is a cycle? What is a phase or an event? And what do these have to do with normalization? We'll answer all of these questions and stay tuned for the end of the video where I'll show some useful tips and software for applying these to your research. With any biomechanical analysis, we need to start with a research question. For the example I'll be using, that is what aspects of technique are associated with running economy? We also need a dependent variable, which in this example will therefore be running economy. And just for a treat, there's me taking part in exactly this type of study a few years ago at Loughborough University. We extract our independent variables from a time series, which is a list of numbers assumed to measure some process sequentially in time. For example, a time series of a joint angle might look something like this. If a movement can be assumed to be periodic and repeat at regular intervals, then the time series can be segmented into cycles for analysis, such as a gate cycle in walking or running. Each cycle starts and ends at a common event, such as initial ground contact. Each event corresponds to a particular time point of interest within the movement and can ideally be automatically identified from ground reaction force thresholds or specified kinematic criteria. The events are used to define and separate the phases of a movement. For example, in running, we have the stance phase, which begins at initial ground contact for that foot and ends at toe off as the same foot leaves the ground. The additional event of mid-stands can be used to split the stance phase into breaking and propulsion phases. The rest of the gate cycle makes up the swing phase, which starts at toe off and ends back as initial contact where the cycle repeats. Mid-swing separates the swing phase into initial and terminal swing. Finally, there are two flight phases when neither foot is in contact with the ground. It's common for studies to extract kinetic or kinematic variables at any of these events, as well as mean or peak values or ranges during any of these phases. And finally, we may consider the timing of an event or the duration of a phase. To see the results of a study that did this for our example dependent variable of running economy, check out this paper, which I'll link to in the description below. When we want to visually compare movement cycles by different individuals or in different conditions, one difficulty to overcome is that each trial will have a different duration. This can make it difficult to compare qualitatively or quantitatively. We can account for these differing movement and phase durations through a process called time normalization, which temporarily aligns each trial. For example, normalizing each time series to 100 values from zero to 100% of the movement or phase. Once the trials have been time normalized, it's common to report the mean time series. However, caution is required when extracting peak values for hypothesis testing. If the peak occurs at a different time point for each trial, then it may be appropriate to extract the peak from each individual trial before averaging those values instead. For an overview of methods of time normalization, see this paper linked below. As well as linear length normalization, it's possible to use piecewise linear length normalization to time normalize individual phases of the movement and temporarily align not only the start and end of the cycle, but also multiple events or key instance during the movement. In this example from my recent flywheel exercise lecture, the eccentric and concentric phases of the squat have been normalized separately. One way of doing this is with the inter-1 function in MATLAB, but if you're not familiar with coding, it's possible to time normalize as well as many other useful functions within the biomechanics toolbar in Excel, which I'll link to in the description below. To analyze the entire time series and not just peaks or means using statistical parametric mapping, check out this six-minute tutorial with no coding experience necessary.